Numerical Solution Of Ordinary And Partial Differential Equations, The (3rd Edition)World Scientific, 16 dic 2014 - 348 pagine This book presents methods for the computational solution of differential equations, both ordinary and partial, time-dependent and steady-state. Finite difference methods are introduced and analyzed in the first four chapters, and finite element methods are studied in chapter five. A very general-purpose and widely-used finite element program, PDE2D, which implements many of the methods studied in the earlier chapters, is presented and documented in Appendix A.The book contains the relevant theory and error analysis for most of the methods studied, but also emphasizes the practical aspects involved in implementing the methods. Students using this book will actually see and write programs (FORTRAN or MATLAB) for solving ordinary and partial differential equations, using both finite differences and finite elements. In addition, they will be able to solve very difficult partial differential equations using the software PDE2D, presented in Appendix A. PDE2D solves very general steady-state, time-dependent and eigenvalue PDE systems, in 1D intervals, general 2D regions, and a wide range of simple 3D regions.The Windows version of PDE2D comes free with every purchase of this book. More information at www.pde2d.com/contact. |
Sommario
| 1 | |
1 Initial Value Ordinary Differential Equations | 27 |
2 The Initial Value Diffusion Problem | 62 |
3 The Initial Value Transport and Wave Problems | 92 |
4 Boundary Value Problems | 121 |
5 The Finite Element Method | 174 |
Appendix ASolving PDEs with PDE2D | 238 |
Altre edizioni - Visualizza tutto
The Numerical Solution of Ordinary and Partial Differential Equations Granville Sewell Anteprima non disponibile - 2015 |
The Numerical Solution of Ordinary and Partial Differential Equations Granville Sewell Anteprima non disponibile - 2014 |
Parole e frasi comuni
absolute value AMAT approximate solution backward difference method band matrix band solver basis functions BMAT boundary conditions boundary value problem calculated collocation method CONTINUE convergence cubic Hermite derivatives diagonal diagonal-dominant difference equation difference formula diffusion DOUBLE PRECISION A-H eigenvalue problem end end ERMAX Euler exact solution explicit method finite difference method finite element method first-order FORTRAN FORTRAN Program FUNA Galerkin method Gaussian elimination grid half-bandwidth IDER IMPLICIT DOUBLE PRECISION INPUT integrals Jacobian KTRI linear system MAXIMUM ERROR multistep method nodes nonlinear nonzero NUMBER OF UNKNOWNS OMEGA ordinary differential equation PARAMETER partial differential equation PDE2D pivoting polynomial positive-definite processors region RETURN END satisfies Section Sewell shown in Figure solve steady-state stepsize stiff subroutine symmetric Theorem time-dependent TKP1 triangle tridiagonal TRIX TRIY truncation error U(t k+1 u(tº U(xi USOL vector XPTS zero