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Biblioteca

MARC Lista (tabellare)
Advances in Numerical Methods for Hyperbolic Balance Laws and Related Problems / / edited by Giacomo Albi, Walter Boscheri, Mattia Zanella
Advances in Numerical Methods for Hyperbolic Balance Laws and Related Problems / / edited by Giacomo Albi, Walter Boscheri, Mattia Zanella
Autore Albi Giacomo
Edizione [1st ed. 2023.]
Pubbl/distr/stampa Cham : , : Springer Nature Switzerland : , : Imprint : Springer, , 2023
Descrizione fisica 1 online resource (241 pages)
Disciplina 004.0151
Altri autori (Persone) BoscheriWalter
ZanellaMattia
Collana SEMA SIMAI Springer Series
Soggetto topico Computer science—Mathematics
Mathematics—Data processing
Neural networks (Computer science)
Mathematical Applications in Computer Science
Computational Mathematics and Numerical Analysis
Mathematical Models of Cognitive Processes and Neural Networks
Equacions diferencials no lineals
Equacions en derivades parcials
Solucions numèriques
Soggetto genere / forma Llibres electrònics
ISBN 3-031-29875-6
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Chapter 1. Alessandro Alla, Peter M. Dower, Vincent Liu. A Tree Structure Approach to Reachability Analysis -- Chapter 2. Giulia Bertaglia. Asymptotic-preserving neural networks for hyperbolic systems with diffusive scaling -- Chapter 3. Felisia Angela Chiarello, Paola Goatin. A non-local system modeling bi-directional traffic flows -- Chapter 4. Armando Coco, Santina Chiara Stissi. Semi-implicit finite-difference methods for compressible gas dynamics with curved boundaries: a ghost-point approach -- Chapter 5. Elena Gaburro, Simone Chiocchetti. High-order arbitrary-Lagrangian-Eulerian schemes on crazy moving Voronoi meshes -- Chapter 6. Elisa Iacomini. Overview on uncertainty quantification in traffic models via intrusive method -- Chapter 7. Liu Liu. A study of multiscale kinetic models with uncertainties -- Chapter 8. Fiammetta Conforto, Giorgio Martalò. On the shock wave discontinuities in Grad hierarchy for a binary mixture of inert gases -- Chapter 9. Giuseppe Visconti, Silvia Tozza, Matteo Semplice, Gabriella Puppo. A conservative a[1]posteriori time-limiting procedure in Quinpi schemes -- Chapter 10. Yuhua Zhu. Applications of Fokker Planck equations in machine learning algorithms.
Record Nr. UNINA-9910728943803321
Albi Giacomo  
Cham : , : Springer Nature Switzerland : , : Imprint : Springer, , 2023
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Anisotropic hp-Mesh adaptation methods : theory, implementation and applications / / Vít Dolejsí and Georg May
Anisotropic hp-Mesh adaptation methods : theory, implementation and applications / / Vít Dolejsí and Georg May
Autore Dolejší Vít
Pubbl/distr/stampa Cham, Switzerland : , : Springer International Publishing, , [2022]
Descrizione fisica 1 online resource (258 pages)
Disciplina 515.353
Collana Nečas Center
Soggetto topico Differential equations, Partial - Numerical solutions
Differential equations, Partial - Numerical solutions - Data processing
Equacions en derivades parcials
Solucions numèriques
Soggetto genere / forma Llibres electrònics
ISBN 3-031-04279-4
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Record Nr. UNISA-996479368203316
Dolejší Vít  
Cham, Switzerland : , : Springer International Publishing, , [2022]
Materiale a stampa
Lo trovi qui: Univ. di Salerno
Opac: Controlla la disponibilità qui
Anisotropic hp-Mesh adaptation methods : theory, implementation and applications / / Vít Dolejsí and Georg May
Anisotropic hp-Mesh adaptation methods : theory, implementation and applications / / Vít Dolejsí and Georg May
Autore Dolejší Vít
Pubbl/distr/stampa Cham, Switzerland : , : Springer International Publishing, , [2022]
Descrizione fisica 1 online resource (258 pages)
Disciplina 515.353
Collana Nečas Center
Soggetto topico Differential equations, Partial - Numerical solutions
Differential equations, Partial - Numerical solutions - Data processing
Equacions en derivades parcials
Solucions numèriques
Soggetto genere / forma Llibres electrònics
ISBN 3-031-04279-4
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Record Nr. UNINA-9910574858103321
Dolejší Vít  
Cham, Switzerland : , : Springer International Publishing, , [2022]
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Bayesian scientific computing / / Daniela Calvetti, Erkki Somersalo
Bayesian scientific computing / / Daniela Calvetti, Erkki Somersalo
Autore Calvetti Daniela
Edizione [1st ed. 2023.]
Pubbl/distr/stampa Cham, Switzerland : , : Springer, , [2023]
Descrizione fisica 1 online resource (295 pages)
Disciplina 519.542
Collana Applied mathematical sciences
Soggetto topico Bayesian statistical decision theory
Inverse problems (Differential equations) - Numerical solutions
Estadística bayesiana
Problemes inversos (Equacions diferencials)
Solucions numèriques
Soggetto genere / forma Llibres electrònics
ISBN 3-031-23824-9
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Inverse problems and subjective computing -- Linear algebra -- Continuous and discrete multivariate distributions -- Introduction to sampling -- The praise of ignorance: randomness as lack of certainty -- Enter subject: Construction of priors -- Posterior densities, ill-conditioning, and classical regularization -- Conditional Gaussian densities -- Iterative linear solvers and priorconditioners -- Hierarchical models and Bayesian sparsity -- Sampling: the real thing -- Dynamic methods and learning from the past -- Bayesian filtering and Gaussian densities -- .
Record Nr. UNINA-9910682585103321
Calvetti Daniela  
Cham, Switzerland : , : Springer, , [2023]
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Equations and inequalities : plain text for non-mathematicians / / Guido Walz
Equations and inequalities : plain text for non-mathematicians / / Guido Walz
Autore Walz Guido
Pubbl/distr/stampa Wiesbaden, Germany : , : Springer, , [2021]
Descrizione fisica 1 online resource (56 pages)
Disciplina 512.94
Collana Springer essentials
Soggetto topico Equacions
Solucions numèriques
Desigualtats (Matemàtica)
Equations - Numerical solutions
Soggetto genere / forma Llibres electrònics
ISBN 3-658-32720-0
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Intro -- What You Can Find in This essential -- Introduction -- Contents -- 1 Equations -- 1.1 What Does an Equation Look Like Anyway? -- 1.2 What Can You Do with an Equation Without Changing Its Solution Set? -- 1.3 Linear Equations -- 1.4 Quadratic Equations -- 1.4.1 First Examples -- 1.4.2 The Midnight Formula -- 1.4.3 The p-q-Formula -- 1.4.4 Quadratic Equations Which Are Not Recognizable at First Glance -- 2 Inequalities -- 2.1 What Kind of Inequalities Are Meant Here? -- 2.2 What Can You Do With an Inequality Without Changing Its Solution Set? -- 2.3 Linear Inequalities -- 2.4 Linear Inequalities That Have Yet to be Sorted -- 2.5 Linear Inequalities That Are Not Immediately Obvious -- 2.6 Fraction Inequalities -- What You Learned From This essential -- References.
Record Nr. UNISA-996466393703316
Walz Guido  
Wiesbaden, Germany : , : Springer, , [2021]
Materiale a stampa
Lo trovi qui: Univ. di Salerno
Opac: Controlla la disponibilità qui
Equations and inequalities : plain text for non-mathematicians / / Guido Walz
Equations and inequalities : plain text for non-mathematicians / / Guido Walz
Autore Walz Guido
Pubbl/distr/stampa Wiesbaden, Germany : , : Springer, , [2021]
Descrizione fisica 1 online resource (56 pages)
Disciplina 512.94
Collana Springer essentials
Soggetto topico Equacions
Solucions numèriques
Desigualtats (Matemàtica)
Equations - Numerical solutions
Soggetto genere / forma Llibres electrònics
ISBN 3-658-32720-0
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Intro -- What You Can Find in This essential -- Introduction -- Contents -- 1 Equations -- 1.1 What Does an Equation Look Like Anyway? -- 1.2 What Can You Do with an Equation Without Changing Its Solution Set? -- 1.3 Linear Equations -- 1.4 Quadratic Equations -- 1.4.1 First Examples -- 1.4.2 The Midnight Formula -- 1.4.3 The p-q-Formula -- 1.4.4 Quadratic Equations Which Are Not Recognizable at First Glance -- 2 Inequalities -- 2.1 What Kind of Inequalities Are Meant Here? -- 2.2 What Can You Do With an Inequality Without Changing Its Solution Set? -- 2.3 Linear Inequalities -- 2.4 Linear Inequalities That Have Yet to be Sorted -- 2.5 Linear Inequalities That Are Not Immediately Obvious -- 2.6 Fraction Inequalities -- What You Learned From This essential -- References.
Record Nr. UNINA-9910488716803321
Walz Guido  
Wiesbaden, Germany : , : Springer, , [2021]
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Geometric Integrators for Differential Equations with Highly Oscillatory Solutions
Geometric Integrators for Differential Equations with Highly Oscillatory Solutions
Autore Wu Xinyuan
Pubbl/distr/stampa Singapore : , : Springer Singapore Pte. Limited, , 2021
Descrizione fisica 1 online resource (507 pages)
Altri autori (Persone) WangBin
Soggetto topico Equacions diferencials
Solucions numèriques
Soggetto genere / forma Llibres electrònics
ISBN 981-16-0147-X
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Intro -- Foreword -- Preface -- Contents -- 1 Oscillation-Preserving Integrators for Highly Oscillatory Systems of Second-Order ODEs -- 1.1 Introduction -- 1.2 Standard Runge-Kutta-Nyström Schemes from the Matrix-Variation-of-Constants Formula -- 1.3 ERKN Integrators and ARKN Methods Based on the Matrix-Variation-of-Constants Formula -- 1.3.1 ARKN Integrators -- 1.3.2 ERKN Integrators -- 1.4 Oscillation-Preserving Integrators -- 1.5 Towards Highly Oscillatory Nonlinear Hamiltonian Systems -- 1.5.1 SSMERKN Integrators -- 1.5.2 Trigonometric Fourier Collocation Methods -- 1.5.3 The AAVF Method and AVF Formula -- 1.6 Other Concerns Relating to Highly Oscillatory Problems -- 1.6.1 Gautschi-Type Methods -- 1.6.2 General ERKN Methods for (1.1) -- 1.6.3 Towards the Application to Semilinear KG Equations -- 1.7 Numerical Experiments -- 1.8 Conclusions and Discussion -- References -- 2 Continuous-Stage ERKN Integrators for Second-Order ODEs with Highly Oscillatory Solutions -- 2.1 Introduction -- 2.2 Extended Runge-Kutta-Nyström Methods -- 2.3 Continuous-Stage ERKN Methods and Order Conditions -- 2.4 Energy-Preserving Conditions and Symmetric Conditions -- 2.5 Linear Stability Analysis -- 2.6 Construction of CSERKN Methods -- 2.6.1 The Case of Order Two -- 2.6.2 The Case of Order Four -- 2.7 Numerical Experiments -- 2.8 Conclusions and Discussions -- References -- 3 Stability and Convergence Analysis of ERKN Integrators for Second-Order ODEs with Highly Oscillatory Solutions -- 3.1 Introduction -- 3.2 Nonlinear Stability and Convergence Analysis for ERKN Integrators -- 3.2.1 Nonlinear Stability of the Matrix-Variation-of-Constants Formula -- 3.2.2 Nonlinear Stability and Convergence of ERKN Integrators -- 3.3 ERKN Integrators with Fourier Pseudospectral Discretisation for Semilinear Wave Equations -- 3.3.1 Time Discretisation: ERKN Time Integrators.
3.3.2 Spatial Discretisation: Fourier Pseudospectral Method -- 3.3.3 Error Bounds of the ERKN-FP Method (3.57)-(3.58) -- 3.4 Numerical Experiments -- 3.5 Conclusions -- References -- 4 Functionally-Fitted Energy-Preserving Integrators for Poisson Systems -- 4.1 Introduction -- 4.2 Functionally-Fitted EP Integrators -- 4.3 Implementation Issues -- 4.4 The Existence, Uniqueness and Smoothness -- 4.5 Algebraic Order -- 4.6 Practical FFEP Integrators -- 4.7 Numerical Experiments -- 4.8 Conclusions -- References -- 5 Exponential Collocation Methods for Conservative or Dissipative Systems -- 5.1 Introduction -- 5.2 Formulation of Methods -- 5.3 Methods for Second-Order ODEs with Highly Oscillatory Solutions -- 5.4 Energy-Preserving Analysis -- 5.5 Existence, Uniqueness and Smoothness of the Solution -- 5.6 Algebraic Order -- 5.7 Application in Stiff Gradient Systems -- 5.8 Practical Examples of Exponential Collocation Methods -- 5.8.1 An Example of ECr Methods -- 5.8.2 An Example of TCr Methods -- 5.8.3 An Example of RKNCr Methods -- 5.9 Numerical Experiments -- 5.10 Concluding Remarks and Discussions -- References -- 6 Volume-Preserving Exponential Integrators -- 6.1 Introduction -- 6.2 Exponential Integrators -- 6.3 VP Condition of Exponential Integrators -- 6.4 VP Results for Different Vector Fields -- 6.4.1 Vector Fields in H -- 6.4.2 Vector Fields in S -- 6.4.3 Vector Fields in F(∞) -- 6.4.4 Vector Fields in F(2) -- 6.5 Applications to Various Problems -- 6.5.1 Highly Oscillatory Second-Order Systems -- 6.5.2 Separable Partitioned Systems -- 6.5.3 Other Applications -- 6.6 Numerical Examples -- 6.7 Conclusions -- References -- 7 Global Error Bounds of One-Stage Explicit ERKN Integrators for Semilinear Wave Equations -- 7.1 Introduction -- 7.2 Preliminaries -- 7.2.1 Spectral Semidiscretisation in Space -- 7.2.2 ERKN Integrators -- 7.3 Main Result.
7.4 The Lower-Order Error Bounds in Higher-Order Sobolev Spaces -- 7.4.1 Regularity Over One Time Step -- 7.4.2 Local Error Bound -- 7.4.3 Stability -- 7.4.4 Proof of Theorem 7.1 for -1 α 0 -- 7.5 Higher-Order Error Bounds in Lower-Order Sobolev Spaces -- 7.6 Numerical Experiments -- 7.7 Concluding Remarks -- References -- 8 Linearly-Fitted Conservative (Dissipative) Schemes for Nonlinear Wave Equations -- 8.1 Introduction -- 8.2 Preliminaries -- 8.3 Extended Discrete Gradient Method -- 8.4 Numerical Experiments -- 8.4.1 Implementation Issues -- 8.4.2 Conservative Wave Equations -- 8.4.3 Dissipative Wave Equations -- 8.5 Conclusions -- References -- 9 Energy-Preserving Schemes for High-Dimensional Nonlinear KG Equations -- 9.1 Introduction -- 9.2 Formulation of Energy-Preserving Schemes -- 9.3 Error Analysis -- 9.4 Analysis of the Nonlinear Stability -- 9.5 Convergence -- 9.6 Implementation Issues of KGDG Scheme -- 9.7 Numerical Experiments -- 9.7.1 One-Dimensional Problems -- 9.7.2 Two-Dimensional Problems -- 9.8 Concluding Remarks -- References -- 10 High-Order Symmetric Hermite-Birkhoff Time Integrators for Semilinear KG Equations -- 10.1 Introduction -- 10.2 The Symmetric and High-Order Hermite-Birkhoff Time Integration Formula -- 10.2.1 The Operator-Variation-of-Constants Formula -- 10.2.2 The Formulation of the Time Integrators -- 10.3 Stability of the Fully Discrete Scheme -- 10.3.1 Linear Stability Analysis -- 10.3.2 Nonlinear Stability Analysis -- 10.4 Convergence of the Fully Discrete Scheme -- 10.4.1 Consistency -- 10.4.2 Convergence -- 10.5 Spatial Discretisation -- 10.6 Waveform Relaxation and Its Convergence -- 10.7 Numerical Experiments -- 10.8 Conclusions and Discussions -- References -- 11 Symplectic Approximations for Efficiently Solving Semilinear KG Equations -- 11.1 Introduction -- 11.2 Abstract Hamiltonian System of ODEs.
11.3 Formulation of the Symplectic Approximation -- 11.3.1 The Time Approximation -- 11.3.2 Symplectic Conditions for the Fully Discrete Scheme -- 11.3.3 Error Analysis of the Extended RKN-Type Approximation -- 11.4 Analysis of the Nonlinear Stability -- 11.5 Convergence -- 11.6 Symplectic Extended RKN-Type Approximation Schemes -- 11.6.1 One-Stage Symplectic Approximation Schemes -- 11.6.2 Two-Stage Symplectic Approximation Schemes -- 11.7 Numerical Experiments -- 11.8 Concluding Remarks -- References -- 12 Continuous-Stage Leap-Frog Schemes for Semilinear Hamiltonian Wave Equations -- 12.1 Introduction -- 12.2 A Continuous-Stage Modified Leap-Frog Scheme -- 12.3 Convergence -- 12.4 Energy-Preserving Continuous-Stage Modified LF Schemes -- 12.5 Symplectic Continuous-Stage Modified LF Scheme -- 12.6 Explicit Continuous-Stage Modified LF Scheme -- 12.7 Numerical Experiments -- 12.8 Conclusions and Discussions -- References -- 13 Semi-Analytical ERKN Integrators for Solving High-Dimensional Nonlinear Wave Equations -- 13.1 Introduction -- 13.2 Preliminaries -- 13.3 Fast Implementation of ERKN Integrators -- 13.4 The Case of Symplectic ERKN Integrators -- 13.5 Analysis of Computational Cost and Memory Usage -- 13.5.1 Computational Cost at Each Time Step -- 13.5.2 Occupied Memory and Maximum Number of Spatial Mesh Grids -- 13.6 Numerical Experiments -- 13.7 Conclusions and Discussions -- References -- 14 Long-Time Momentum and Actions Behaviour of Energy-Preserving Methods for Wave Equations -- 14.1 Introduction -- 14.2 Full Discretisation -- 14.2.1 Spectral Semidiscretisation in Space -- 14.2.2 EP Methods in Time -- 14.3 Main Result and Numerical Experiment -- 14.3.1 Main Result -- 14.3.2 Numerical Experiments -- 14.4 The Proof of the Main Result -- 14.4.1 The Outline of the Proof -- 14.4.2 Modulation Equations -- 14.4.3 Reverse Picard Iteration.
14.4.4 Rescaling and Estimation of the Nonlinear Terms -- 14.4.5 Reformulation of the Reverse Picard Iteration -- 14.4.6 Bounds of the Coefficient Functions -- 14.4.7 Defects -- 14.4.8 Remainders -- 14.4.9 Almost Invariants -- 14.4.10 From Short to Long-Time Intervals -- 14.5 Analysis for the AAVF Method with a Quadrature Rule -- 14.6 Conclusions and Discussions -- References -- Index.
Record Nr. UNISA-996466398403316
Wu Xinyuan  
Singapore : , : Springer Singapore Pte. Limited, , 2021
Materiale a stampa
Lo trovi qui: Univ. di Salerno
Opac: Controlla la disponibilità qui
Geometric Integrators for Differential Equations with Highly Oscillatory Solutions
Geometric Integrators for Differential Equations with Highly Oscillatory Solutions
Autore Wu Xinyuan
Pubbl/distr/stampa Singapore : , : Springer Singapore Pte. Limited, , 2021
Descrizione fisica 1 online resource (507 pages)
Altri autori (Persone) WangBin
Soggetto topico Equacions diferencials
Solucions numèriques
Soggetto genere / forma Llibres electrònics
ISBN 981-16-0147-X
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Intro -- Foreword -- Preface -- Contents -- 1 Oscillation-Preserving Integrators for Highly Oscillatory Systems of Second-Order ODEs -- 1.1 Introduction -- 1.2 Standard Runge-Kutta-Nyström Schemes from the Matrix-Variation-of-Constants Formula -- 1.3 ERKN Integrators and ARKN Methods Based on the Matrix-Variation-of-Constants Formula -- 1.3.1 ARKN Integrators -- 1.3.2 ERKN Integrators -- 1.4 Oscillation-Preserving Integrators -- 1.5 Towards Highly Oscillatory Nonlinear Hamiltonian Systems -- 1.5.1 SSMERKN Integrators -- 1.5.2 Trigonometric Fourier Collocation Methods -- 1.5.3 The AAVF Method and AVF Formula -- 1.6 Other Concerns Relating to Highly Oscillatory Problems -- 1.6.1 Gautschi-Type Methods -- 1.6.2 General ERKN Methods for (1.1) -- 1.6.3 Towards the Application to Semilinear KG Equations -- 1.7 Numerical Experiments -- 1.8 Conclusions and Discussion -- References -- 2 Continuous-Stage ERKN Integrators for Second-Order ODEs with Highly Oscillatory Solutions -- 2.1 Introduction -- 2.2 Extended Runge-Kutta-Nyström Methods -- 2.3 Continuous-Stage ERKN Methods and Order Conditions -- 2.4 Energy-Preserving Conditions and Symmetric Conditions -- 2.5 Linear Stability Analysis -- 2.6 Construction of CSERKN Methods -- 2.6.1 The Case of Order Two -- 2.6.2 The Case of Order Four -- 2.7 Numerical Experiments -- 2.8 Conclusions and Discussions -- References -- 3 Stability and Convergence Analysis of ERKN Integrators for Second-Order ODEs with Highly Oscillatory Solutions -- 3.1 Introduction -- 3.2 Nonlinear Stability and Convergence Analysis for ERKN Integrators -- 3.2.1 Nonlinear Stability of the Matrix-Variation-of-Constants Formula -- 3.2.2 Nonlinear Stability and Convergence of ERKN Integrators -- 3.3 ERKN Integrators with Fourier Pseudospectral Discretisation for Semilinear Wave Equations -- 3.3.1 Time Discretisation: ERKN Time Integrators.
3.3.2 Spatial Discretisation: Fourier Pseudospectral Method -- 3.3.3 Error Bounds of the ERKN-FP Method (3.57)-(3.58) -- 3.4 Numerical Experiments -- 3.5 Conclusions -- References -- 4 Functionally-Fitted Energy-Preserving Integrators for Poisson Systems -- 4.1 Introduction -- 4.2 Functionally-Fitted EP Integrators -- 4.3 Implementation Issues -- 4.4 The Existence, Uniqueness and Smoothness -- 4.5 Algebraic Order -- 4.6 Practical FFEP Integrators -- 4.7 Numerical Experiments -- 4.8 Conclusions -- References -- 5 Exponential Collocation Methods for Conservative or Dissipative Systems -- 5.1 Introduction -- 5.2 Formulation of Methods -- 5.3 Methods for Second-Order ODEs with Highly Oscillatory Solutions -- 5.4 Energy-Preserving Analysis -- 5.5 Existence, Uniqueness and Smoothness of the Solution -- 5.6 Algebraic Order -- 5.7 Application in Stiff Gradient Systems -- 5.8 Practical Examples of Exponential Collocation Methods -- 5.8.1 An Example of ECr Methods -- 5.8.2 An Example of TCr Methods -- 5.8.3 An Example of RKNCr Methods -- 5.9 Numerical Experiments -- 5.10 Concluding Remarks and Discussions -- References -- 6 Volume-Preserving Exponential Integrators -- 6.1 Introduction -- 6.2 Exponential Integrators -- 6.3 VP Condition of Exponential Integrators -- 6.4 VP Results for Different Vector Fields -- 6.4.1 Vector Fields in H -- 6.4.2 Vector Fields in S -- 6.4.3 Vector Fields in F(∞) -- 6.4.4 Vector Fields in F(2) -- 6.5 Applications to Various Problems -- 6.5.1 Highly Oscillatory Second-Order Systems -- 6.5.2 Separable Partitioned Systems -- 6.5.3 Other Applications -- 6.6 Numerical Examples -- 6.7 Conclusions -- References -- 7 Global Error Bounds of One-Stage Explicit ERKN Integrators for Semilinear Wave Equations -- 7.1 Introduction -- 7.2 Preliminaries -- 7.2.1 Spectral Semidiscretisation in Space -- 7.2.2 ERKN Integrators -- 7.3 Main Result.
7.4 The Lower-Order Error Bounds in Higher-Order Sobolev Spaces -- 7.4.1 Regularity Over One Time Step -- 7.4.2 Local Error Bound -- 7.4.3 Stability -- 7.4.4 Proof of Theorem 7.1 for -1 α 0 -- 7.5 Higher-Order Error Bounds in Lower-Order Sobolev Spaces -- 7.6 Numerical Experiments -- 7.7 Concluding Remarks -- References -- 8 Linearly-Fitted Conservative (Dissipative) Schemes for Nonlinear Wave Equations -- 8.1 Introduction -- 8.2 Preliminaries -- 8.3 Extended Discrete Gradient Method -- 8.4 Numerical Experiments -- 8.4.1 Implementation Issues -- 8.4.2 Conservative Wave Equations -- 8.4.3 Dissipative Wave Equations -- 8.5 Conclusions -- References -- 9 Energy-Preserving Schemes for High-Dimensional Nonlinear KG Equations -- 9.1 Introduction -- 9.2 Formulation of Energy-Preserving Schemes -- 9.3 Error Analysis -- 9.4 Analysis of the Nonlinear Stability -- 9.5 Convergence -- 9.6 Implementation Issues of KGDG Scheme -- 9.7 Numerical Experiments -- 9.7.1 One-Dimensional Problems -- 9.7.2 Two-Dimensional Problems -- 9.8 Concluding Remarks -- References -- 10 High-Order Symmetric Hermite-Birkhoff Time Integrators for Semilinear KG Equations -- 10.1 Introduction -- 10.2 The Symmetric and High-Order Hermite-Birkhoff Time Integration Formula -- 10.2.1 The Operator-Variation-of-Constants Formula -- 10.2.2 The Formulation of the Time Integrators -- 10.3 Stability of the Fully Discrete Scheme -- 10.3.1 Linear Stability Analysis -- 10.3.2 Nonlinear Stability Analysis -- 10.4 Convergence of the Fully Discrete Scheme -- 10.4.1 Consistency -- 10.4.2 Convergence -- 10.5 Spatial Discretisation -- 10.6 Waveform Relaxation and Its Convergence -- 10.7 Numerical Experiments -- 10.8 Conclusions and Discussions -- References -- 11 Symplectic Approximations for Efficiently Solving Semilinear KG Equations -- 11.1 Introduction -- 11.2 Abstract Hamiltonian System of ODEs.
11.3 Formulation of the Symplectic Approximation -- 11.3.1 The Time Approximation -- 11.3.2 Symplectic Conditions for the Fully Discrete Scheme -- 11.3.3 Error Analysis of the Extended RKN-Type Approximation -- 11.4 Analysis of the Nonlinear Stability -- 11.5 Convergence -- 11.6 Symplectic Extended RKN-Type Approximation Schemes -- 11.6.1 One-Stage Symplectic Approximation Schemes -- 11.6.2 Two-Stage Symplectic Approximation Schemes -- 11.7 Numerical Experiments -- 11.8 Concluding Remarks -- References -- 12 Continuous-Stage Leap-Frog Schemes for Semilinear Hamiltonian Wave Equations -- 12.1 Introduction -- 12.2 A Continuous-Stage Modified Leap-Frog Scheme -- 12.3 Convergence -- 12.4 Energy-Preserving Continuous-Stage Modified LF Schemes -- 12.5 Symplectic Continuous-Stage Modified LF Scheme -- 12.6 Explicit Continuous-Stage Modified LF Scheme -- 12.7 Numerical Experiments -- 12.8 Conclusions and Discussions -- References -- 13 Semi-Analytical ERKN Integrators for Solving High-Dimensional Nonlinear Wave Equations -- 13.1 Introduction -- 13.2 Preliminaries -- 13.3 Fast Implementation of ERKN Integrators -- 13.4 The Case of Symplectic ERKN Integrators -- 13.5 Analysis of Computational Cost and Memory Usage -- 13.5.1 Computational Cost at Each Time Step -- 13.5.2 Occupied Memory and Maximum Number of Spatial Mesh Grids -- 13.6 Numerical Experiments -- 13.7 Conclusions and Discussions -- References -- 14 Long-Time Momentum and Actions Behaviour of Energy-Preserving Methods for Wave Equations -- 14.1 Introduction -- 14.2 Full Discretisation -- 14.2.1 Spectral Semidiscretisation in Space -- 14.2.2 EP Methods in Time -- 14.3 Main Result and Numerical Experiment -- 14.3.1 Main Result -- 14.3.2 Numerical Experiments -- 14.4 The Proof of the Main Result -- 14.4.1 The Outline of the Proof -- 14.4.2 Modulation Equations -- 14.4.3 Reverse Picard Iteration.
14.4.4 Rescaling and Estimation of the Nonlinear Terms -- 14.4.5 Reformulation of the Reverse Picard Iteration -- 14.4.6 Bounds of the Coefficient Functions -- 14.4.7 Defects -- 14.4.8 Remainders -- 14.4.9 Almost Invariants -- 14.4.10 From Short to Long-Time Intervals -- 14.5 Analysis for the AAVF Method with a Quadrature Rule -- 14.6 Conclusions and Discussions -- References -- Index.
Record Nr. UNINA-9910503005503321
Wu Xinyuan  
Singapore : , : Springer Singapore Pte. Limited, , 2021
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Graded finite element methods for elliptic problems in nonsmooth domains / / Hengguang Li
Graded finite element methods for elliptic problems in nonsmooth domains / / Hengguang Li
Autore Li Hengguang
Pubbl/distr/stampa Cham, Switzerland : , : Springer, , [2022]
Descrizione fisica 1 online resource (186 pages)
Disciplina 515.35
Collana Surveys and Tutorials in the Applied Mathematical Sciences
Soggetto topico Boundary value problems
Problemes de contorn
Solucions numèriques
Equacions diferencials
Soggetto genere / forma Llibres electrònics
ISBN 9783031058219
9783031058202
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Record Nr. UNISA-996490347803316
Li Hengguang  
Cham, Switzerland : , : Springer, , [2022]
Materiale a stampa
Lo trovi qui: Univ. di Salerno
Opac: Controlla la disponibilità qui
Graded finite element methods for elliptic problems in nonsmooth domains / / Hengguang Li
Graded finite element methods for elliptic problems in nonsmooth domains / / Hengguang Li
Autore Li Hengguang
Pubbl/distr/stampa Cham, Switzerland : , : Springer, , [2022]
Descrizione fisica 1 online resource (186 pages)
Disciplina 515.35
Collana Surveys and Tutorials in the Applied Mathematical Sciences
Soggetto topico Boundary value problems
Problemes de contorn
Solucions numèriques
Equacions diferencials
Soggetto genere / forma Llibres electrònics
ISBN 9783031058219
9783031058202
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Record Nr. UNINA-9910591038503321
Li Hengguang  
Cham, Switzerland : , : Springer, , [2022]
Materiale a stampa
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