The Numerical Solution of Ordinary and Partial Differential EquationsJohn Wiley & Sons, 25 lug 2005 - 352 pagine Learn to write programs to solve ordinary and partial differential equations The Second Edition of this popular text provides an insightful introduction to the use of finite difference and finite element methods for the computational solution of ordinary and partial differential equations. Readers gain a thorough understanding of the theory underlying themethods presented in the text. The author emphasizes the practical steps involved in implementing the methods, culminating in readers learning how to write programs using FORTRAN90 and MATLAB(r) to solve ordinary and partial differential equations. The book begins with a review of direct methods for the solution of linear systems, with an emphasis on the special features of the linear systems that arise when differential equations are solved. The following four chapters introduce and analyze the more commonly used finite difference methods for solving a variety of problems, including ordinary and partial differential equations and initial value and boundary value problems. The techniques presented in these chapters, with the aid of carefully developed exercises and numerical examples, can be easilymastered by readers. The final chapter of the text presents the basic theory underlying the finite element method. Following the guidance offered in this chapter, readers gain a solid understanding of the method and discover how to use it to solve many problems. A special feature of the Second Edition is Appendix A, which describes a finite element program, PDE2D, developed by the author. Readers discover how PDE2D can be used to solve difficult partial differential equation problems, including nonlinear time-dependent and steady-state systems, and linear eigenvalue systems in 1D intervals, general 2D regions, and a wide range of simple 3D regions. The software itself is available to instructors who adopt the text to share with their students. |
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Altre edizioni - Visualizza tutto
The Numerical Solution of Ordinary and Partial Differential Equations Granville Sewell Anteprima limitata - 2014 |
The Numerical Solution of Ordinary and Partial Differential Equations Granville Sewell Visualizzazione estratti - 1988 |
The Numerical Solution of Ordinary and Partial Differential Equations Granville Sewell Anteprima non disponibile - 2005 |
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accuracy applied approximate assumed band band solver basis functions bound boundary conditions boundary value calculated called characteristic chosen coefficients collocation column compared Consider constant CONTINUE convergence defined depends derivatives diagonal difference method diffusion direct DOUBLE eigenvalue elimination end end equal ERMAX EVALUATE exact solution example explicit method fact Figure finite difference first formula FORTRAN Galerkin given global grid implicit initial value INPUT integrals inverse iteration less linear system matrix maximum memory multiple nonlinear nonzero normal Note OMEGA ooo ooo ordinary differential equation PARAMETER partial differential equation PDE2D pivoting polynomial positive positive-definite processors region RETURN satisfies satisfy shown shows side simple solution solve space stability starting step stepsize stiff subroutine symmetric Table Theorem triangle truncation error unknowns value problem vector zero