Autore	Vabishchevich P. N (Petr Nikolaevich)
Pubbl/distr/stampa	Berlin ; ; Boston : , : Walter de Gruyter GmbH & Co. KG, , [2014]
Descrizione fisica	1 online resource (370 p.)
Disciplina	515/.724
Soggetto topico	Initial value problems Boundary value problems Differential operators Mathematical models
Soggetto genere / forma	Electronic books.
ISBN	3-11-032146-7
Classificazione	SK 920
Formato	Materiale a stampa
Livello bibliografico	Monografia
Lingua di pubblicazione	eng
Nota di contenuto	Front matter -- Preface -- Contents -- Notation -- 1. Introduction -- 2. Stability of operator-difference schemes -- 3. Operator splitting -- 4. Additive schemes of two-component splitting -- 5. Schemes of summarized approximation -- 6. Regularized additive schemes -- 7. Schemes based on approximations of a transition operator -- 8. Vector additive schemes -- 9. Iterative methods -- 10. Splitting of the operator at the time derivative -- 11 Equations with pairwise adjoint operators -- Bibliography -- Index
Record Nr.	UNINA-9910453789403321

Pubbl/distr/stampa	Berlin, : De Gruyter, 2012
Descrizione fisica	1 online resource (552 p.)
Disciplina	515 515.35 515/.35
Altri autori (Persone)	WangYanfei <1973-> YagolaA. G YangChangchun <1945->
Collana	Inverse and ill-posed problems series
Soggetto topico	Inverse problems (Differential equations) - Numerical solutions Differential equations - Numerical solutions
Soggetto genere / forma	Electronic books.
ISBN	1-283-85670-0 3-11-025905-2
Classificazione	SK 920
Formato	Materiale a stampa
Livello bibliografico	Monografia
Lingua di pubblicazione	eng
Nota di contenuto	Front matter -- Preface -- Editor's Preface -- Contents -- Part I. Introduction -- Chapter 1. Inverse Problems of Mathematical Physics / Kabanikhin, S. I. -- Part II. Recent Advances in Regularization Theory and Methods -- Chapter 2. Using Parallel Computing for Solving Multidimensional Ill-posed Problems / Lukyanenko, D. V. / Yagola, A. G. -- Chapter 3. Regularization of Fredholm Integral Equations of the First Kind using Nyström Approximation / Nair, M. T. -- Chapter 4. Regularization of Numerical Differentiation: Methods and Applications / Xiao, T. Y. / Zhang, H. / Hao, L. L. -- Chapter 5. Numerical Analytic Continuation and Regularization / Fu, C. L. / Cheng, H. / Ma, Y. J. -- Chapter 6. An Optimal Perturbation Regularization Algorithm for Function Reconstruction and Its Applications / Li, G. S. -- Chapter 7. Filtering and Inverse Problems Solving / Zotov, L. V. / Panteleev, V. L. -- Part III. Optimal Inverse Design and Optimization Methods -- Chapter 8. Inverse Design of Alloys' Chemistry for Specified Thermo-Mechanical Properties by using Multi-objective Optimization / Dulikravich, G. S. / Egorov, I. N. -- Chapter 9. Two Approaches to Reduce the Parameter Identification Errors / Xiang, Z. H. -- Chapter 10. A General Convergence Result for the BFGS Method / Dai, Y. H. -- Part IV. Recent Advances in Inverse Scattering -- Chapter 11. Uniqueness Results for Inverse Scattering Problems / Liu, X. D. / Zhang, B. -- Chapter 12. Shape Reconstruction of Inverse Medium Scattering for the Helmholtz Equation / Bao, G. / Li, P. J. -- Part V. Inverse Vibration, Data Processing and Imaging -- Chapter 13. Numerical Aspects of the Calculation of Molecular Force Fields from Experimental Data / Kuramshina, G. M. / Kochikov, I. V. / Stepanova, A. V. -- Chapter 14. Some Mathematical Problems in Biomedical Imaging / Liu, J. J. / Xu, H. L. -- Part VI Numerical Inversion in Geosciences -- Chapter 15. Numerical Methods for Solving Inverse Hyperbolic Problems / Kabanikhin, S. I. / Shishlenin, M. A. -- Chapter 16. Inversion Studies in Seismic Oceanography / Song, H. B. / Huang, X. H. / Pinheiro, L. M. / Song, Y. / Dong, C. Z. / Bai, Y. -- Chapter 17. Image Resolution Beyond the Classical Limit / Gelius, L. J. -- Chapter 18. Seismic Migration and Inversion / Wang, Y. F. / Li, Z. H. / Yang, C. C. -- Chapter 19. Seismic Wavefields Interpolation Based on Sparse Regularization and Compressive Sensing / Wang, Y. F. / Cao, J. J. / Sun, T. / Yang, C. C. -- Chapter 20. Some Researches on Quantitative Remote Sensing Inversion / Yang, H. -- Index
Record Nr.	UNINA-9910462635203321

Autore	Lorenzi A.
Edizione	[Reprint 2014]
Pubbl/distr/stampa	Utrecht ; ; Boston : , : VSP, , 2001
Descrizione fisica	1 online resource (254 pages) : illustrations
Disciplina	515/.7
Collana	Inverse and ill-posed problems series
Soggetto topico	Inverse problems (Differential equations) Functional analysis
Soggetto genere / forma	Electronic books.
ISBN	3-11-094092-2
Classificazione	SK 920
Formato	Materiale a stampa
Livello bibliografico	Monografia
Lingua di pubblicazione	eng
Nota di contenuto	Frontmatter -- Preface -- Contents -- Introduction -- Chapter 1. Parameter Identification In Linear Ordinary Differential Equations -- Chapter 2. Identification Problems In Hilbert Spaces -- Chapter 3. Proper Riemann Integrals For Banach-Valued Functions. Curvilinear Integrals And Banach-Valued Holomorphic Functions -- Chapter 4. Riemann-Stieltj Es Integrals Of Banach-Valued Functions -- Chapter 5. Improper Riemann Integrals For Banach Space-Valued Functions -- Chapter 6. Banach Algebras And Spectral Analysis For Linear Bounded Operators -- Chapter 7. Identifying Parameters In First-Order Partial Differential Equations -- Chapter 8. Identification Problems Relative To Linear Bounded Operators I -- Chapter 9. Identification Problems Relative To Linear Bounded Operators Ii -- Chapter 10. Analysis Of The Continuous Dependence On The Data -- Chapter 11. Linear Closed Operators And Analytic Semigroups Of Linear Bounded Operators -- Chapter 12. Cauchy Problems For Linear Abstract Differential Equations Relative To Sectorial Operators And Applications -- Chapter 13. Identification Problems For Linear Abstract Differential Equations Relative To Sectorial Operators And Applications -- Bibliography -- List of Symbols
Record Nr.	UNINA-9910463727703321

Pubbl/distr/stampa	Singapore ; ; Hackensack, N.J., : World Scientific, c2012
Descrizione fisica	1 online resource (285 p.)
Disciplina	620.11015118 620.1127
Altri autori (Persone)	BaoWeizhu DuQiang
Collana	Lecture notes series / Institute for Mathematical Sciences, National University of Singapore
Soggetto topico	Multiscale modeling - Computer simulation Materials - Analysis - Mathematical models Materials - Analysis - Computer simulation
ISBN	1-280-37645-7 9786613555427 981-4360-90-2
Classificazione	SK 920 SK 950
Formato	Materiale a stampa
Livello bibliografico	Monografia
Lingua di pubblicazione	eng
Nota di contenuto	CONTENTS; Foreword; Preface; Dislocation Dynamics in 2 + Dimensions: Slip Planes, Thin Films, and Grain Boundaries Yang Xiang, Siu Sin Quek, Yong-Wei Zhang, Adele T. Lim and David J. Srolovitz; Contents; 1. Introduction; 2. Peierls-Nabarro models for dislocations; 2.1. Classical Peierls-Nabarro model for straight dislocations; 2.2. Generalizations of Peierls-Nabarro model for straight dislocations; 2.3. Generalizations to curved dislocations; 2.4. From the Peierls-Nabarro model to a continuum dislocation dynamics model in a slip plane 2.5. Conclusions of Peierls-Nabarro models of dislocations3. Dislocation dynamics in thin films; 3.1. Dislocation dynamics simulation in thin film: A brief review; 3.1.1. Front-tracking methods; Two dimensions; Three dimensions; 3.1.2. Phase field method; 3.1.3. Level set method; 3.2. Level set simulation of dislocation dynamics in thin films; 3.2.1. Dislocation half-loop in a stationary film; 3.2.2. Pair of coplanar identical half-loops in a stationary film; 3.2.3. Non-identical coplanar half-loops in a stationary film 3.2.4. Dislocation half-loops on intersecting glide planes in a stationary film3.2.5. Dislocation evolution during single-layer film growth; 3.2.6. Dislocation evolution during bilayer film growth; 3.3. Conclusions of dislocation dynamics in thin films; 4. Dislocation models for low-angle grain boundary migration; 4.1. Introduction to dislocation models for LAGBs; 4.2. Simulation model and method for LAGB migration; 4.2.1. 2-d dislocation dynamics for LAGB migration; 4.2.2. 3-d dislocation dynamics for LAGB migration; 4.3. 2-d dislocation dynamics simulation results 4.3.1. One set of intrinsic dislocations4.3.2. One set of intrinsic dislocations + extrinsic dislocations; 4.3.3. Two sets of intrinsic dislocations; 4.4. 3-d dislocation dynamics simulation results; 4.4.1. Two sets of intersecting intrinsic dislocations; 4.4.2. Mixed LAGB + extrinsic dislocations; 4.5. Conclusions of dislocation models for LAGB migration; 5. Conclusions; Acknowledgments; References; Introduction to Molecular Dynamics Simulations Xiantao Li; Contents; 1. Introduction; 2. Statistical mechanics basis; 2.1. Micro-canonical (NVE) ensemble; 2.2. Canonical (NVT) ensemble 2.3. Modeling canonical ensemble2.4. Linear response and dynamic quantities; 3. Numerical methods for molecular dynamics simulation; 3.1. Non-dimensionalization; 3.2. Time integration for Hamiltonian systems; 3.3. Force calculation; 3.4. Boundary conditions; 4. Non-equilibrium molecular dynamics models; 4.1. Boundary condition for non-equilibrium molecular dynamics; 4.1.1. Exact boundary condition; 4.2. Exact boundary condition; 4.2.1. Approximate boundary condition; 4.2.2. Finite temperature boundary condition; 4.3. Coarse-grained molecular dynamics model; 4.4. A one-dimensional example 5. Summary and discussions
Record Nr.	UNINA-9910778818003321

Autore	Atkinson Kendall E.
Pubbl/distr/stampa	Hoboken, New Jersey : , : Wiley, , 2009
Descrizione fisica	1 online resource (272 p.)
Disciplina	515.352
Collana	Pure and Applied Mathematics: A Wiley-Interscience Series of Texts, Monographs, and Tracts
Soggetto topico	Differential equations - Numerical solutions
ISBN	1-283-33249-3 9786613332493 1-118-16449-0 1-118-16452-0
Classificazione	SK 920
Formato	Materiale a stampa
Livello bibliografico	Monografia
Lingua di pubblicazione	eng
Nota di contenuto	Numerical Solution of Ordinary Differential Equations; CONTENTS; Introduction; 1 Theory of differential equations: An introduction; 1.1 General solvability theory; 1.2 Stability of the initial value problem; 1.3 Direction fields; Problems; 2 Euler's method; 2.1 Definition of Euler's method; 2.2 Error analysis of Euler's method; 2.3 Asymptotic error analysis; 2.3.1 Richardson extrapolation; 2.4 Numerical stability; 2.4.1 Rounding error accumulation; Problems; 3 Systems of differential equations; 3.1 Higher-order differential equations; 3.2 Numerical methods for systems; Problems 4 The backward Euler method and the trapezoidal method4.1 The backward Euler method; 4.2 The trapezoidal method; Problems; 5 Taylor and Runge-Kutta methods; 5.1 Taylor methods; 5.2 Runge-Kutta methods; 5.2.1 A general framework for explicit Runge-Kutta methods; 5.3 Convergence, stability, and asymptotic error; 5.3.1 Error prediction and control; 5.4 Runge-Kutta-Fehlberg methods; 5.5 MATLAB codes; 5.6 Implicit Runge-Kutta methods; 5.6.1 Two-point collocation methods; Problems; 6 Multistep methods; 6.1 Adams-Bashforth methods; 6.2 Adams-Moulton methods; 6.3 Computer codes 6.3.1 MATLAB ODE codesProblems; 7 General error analysis for multistep methods; 7.1 Truncation error; 7.2 Convergence; 7.3 A general error analysis; 7.3.1 Stability theory; 7.3.2 Convergence theory; 7.3.3 Relative stability and weak stability; Problems; 8 Stiff differential equations; 8.1 The method of lines for a parabolic equation; 8.1.1 MATLAB programs for the method of lines; 8.2 Backward differentiation formulas; 8.3 Stability regions for multistep methods; 8.4 Additional sources of difficulty; 8.4.1 A-stability and L-stability; 8.4.2 Time-varying problems and stability 8.5 Solving the finite-difference method8.6 Computer codes; Problems; 9 Implicit RK methods for stiff differential equations; 9.1 Families of implicit Runge-Kutta methods; 9.2 Stability of Runge-Kutta methods; 9.3 Order reduction; 9.4 Runge-Kutta methods for stiff equations in practice; Problems; 10 Differential algebraic equations; 10.1 Initial conditions and drift; 10.2 DAEs as stiff differential equations; 10.3 Numerical issues: higher index problems; 10.4 Backward differentiation methods for DAEs; 10.4.1 Index 1 problems; 10.4.2 Index 2 problems; 10.5 Runge-Kutta methods for DAEs 10.5.1 Index 1 problems10.5.2 Index 2 problems; 10.6 Index three problems from mechanics; 10.6.1 Runge-Kutta methods for mechanical index 3 systems; 10.7 Higher index DAEs; Problems; 11 Two-point boundary value problems; 11.1 A finite-difference method; 11.1.1 Convergence; 11.1.2 A numerical example; 11.1.3 Boundary conditions involving the derivative; 11.2 Nonlinear two-point boundary value problems; 11.2.1 Finite difference methods; 11.2.2 Shooting methods; 11.2.3 Collocation methods; 11.2.4 Other methods and problems; Problems; 12 Volterra integral equations; 12.1 Solvability theory 12.1.1 Special equations
Record Nr.	UNINA-9910141193403321