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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 | ||
| ||
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 |
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Wu Xinyuan
|
||
| Singapore : , : Springer Singapore Pte. Limited, , 2021 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Recent Developments in Structure-Preserving Algorithms for Oscillatory Differential Equations / / by Xinyuan Wu, Bin Wang
| Recent Developments in Structure-Preserving Algorithms for Oscillatory Differential Equations / / by Xinyuan Wu, Bin Wang |
| Autore | Wu Xinyuan |
| Edizione | [1st ed. 2018.] |
| Pubbl/distr/stampa | Singapore : , : Springer Singapore : , : Imprint : Springer, , 2018 |
| Descrizione fisica | 1 online resource (356 pages) |
| Disciplina | 515.35 |
| Soggetto topico |
Algorithms
Computational complexity Mathematics of Algorithmic Complexity Complexity |
| ISBN | 981-10-9004-1 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Functionally fitted continuous finite element methods for oscillatory Hamiltonian system -- Exponential average-vector-field integrator for conservative or dissipative systems -- Exponential Fourier collocation methods for first-order differential Equations -- Symplectic exponential Runge-Kutta methods for solving nonlinear Hamiltonian systems -- High-order symplectic and symmetric composition integrators for multi-frequency oscillatory Hamiltonian systems -- The construction of arbitrary order ERKN integrators via group theory -- Trigonometric collocation methods for multi-frequency and multidimensional oscillatory systems -- A compact tri-colored tree theory for general ERKN methods -- An integral formula adapted to different boundary conditions for arbitrarily high-dimensional nonlinear Klein-Gordon equations -- An energy-preserving and symmetric scheme for nonlinear Hamiltonian wave equations -- Arbitrarily high-order time-stepping schemes for nonlinear Klein–Gordon equations -- An essential extension of the finite-energy condition for ERKN integrators solving nonlinear wave equations -- Index. |
| Record Nr. | UNINA-9910300123603321 |
|
Wu Xinyuan
|
||
| Singapore : , : Springer Singapore : , : Imprint : Springer, , 2018 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Structure-preserving algorithms for oscillatory differential equations / / Xinyuan Wu, Xiong You, Bin Wang
| Structure-preserving algorithms for oscillatory differential equations / / Xinyuan Wu, Xiong You, Bin Wang |
| Autore | Wu Xinyuan |
| Edizione | [1st ed. 2013.] |
| Pubbl/distr/stampa | Heidelberg ; ; New York, : Springer |
| Descrizione fisica | 1 online resource (xii, 236 pages) : illustrations |
| Disciplina | 511.8 |
| Altri autori (Persone) |
YouXiong
WangBin |
| Collana | Gale eBooks |
| Soggetto topico |
Differential equations, Nonlinear - Numerical solutions
Mathematics |
| ISBN |
1-299-33711-2
3-642-35338-X |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Runge-Kutta (-Nyström) Methods for Oscillatory Differential Equations -- ARKN Methods -- ERKN Methods -- Symplectic and Symmetric Multidimensional ERKN Methods -- Two-Step Multidimensional ERKN Methods -- Adapted Falkner-Type Methods -- Energy-Preserving ERKN Methods -- Effective Methods for Highly Oscillatory Second-Order Nonlinear Differential Equations -- Extended Leap-Frog Methods for Hamiltonian Wave Equations. |
| Record Nr. | UNINA-9910437886703321 |
|
Wu Xinyuan
|
||
| Heidelberg ; ; New York, : Springer | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Structure-preserving algorithms for oscillatory differential equations II / / by Xinyuan Wu, Kai Liu, Wei Shi
| Structure-preserving algorithms for oscillatory differential equations II / / by Xinyuan Wu, Kai Liu, Wei Shi |
| Autore | Wu Xinyuan |
| Edizione | [1st ed. 2015.] |
| Pubbl/distr/stampa | Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 2015 |
| Descrizione fisica | 1 online resource (305 p.) |
| Disciplina | 620 |
| Soggetto topico |
Applied mathematics
Engineering mathematics Mathematical physics Computer mathematics Mathematical and Computational Engineering Theoretical, Mathematical and Computational Physics Computational Science and Engineering |
| ISBN | 3-662-48156-1 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Matrix-variation-of-constants formula -- Improved St ¨ormer-Verlet formulae with applications -- Improved Filon-type asymptotic methods for highly oscillatory differential equations -- Efficient energy-preserving integrators for multi-frequency oscillatory Hamiltonian systems -- An extended discrete gradient formula for multi-frequency oscillatory Hamiltonian systems -- Trigonometric Fourier collocation methods for multi-frequency oscillatory systems -- Error bounds for explicit ERKN integrators for multi-frequency oscillatory systems -- Error analysis of explicit TSERKN methods for highly oscillatory systems -- Highly accurate explicit symplectic ERKN methods for multi-frequency oscillatory Hamiltonian systems -- Multidimensional ARKN methods for general multi-frequency oscillatory second-order IVPs -- A simplified Nystr¨om-tree theory for ERKN integrators solving oscillatory systems -- An efficient high-order explicit scheme for solving Hamiltonian nonlinear wave equations. |
| Record Nr. | UNINA-9910299673603321 |
|
Wu Xinyuan
|
||
| Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 2015 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||