Numerical Methods for Differential Equations A Computational Approach

With emphasis on modern techniques, Numerical Methods for Differential Equations: A Computational Approach covers the development and application of methods for the numerical solution of ordinary differential equations. Some of the methods are extended to cover partial differential equations. All techniques covered in the text are on a disk included with the book, and are written in FORTRAN 90. These programs are ideal for students, researchers, and other practitioners because they allow for straightforward application of the numerical methods described in the text. The code is easily modified to solve new systems of equations. Numerical Methods for Differential Equations: A Computational Approach also contains what is probably the first reliable and inexpensive global error code to be made available to practitioners who are interested in global error estimation. This is a valuable text for students, who will find the derivations of the numerical methods extremely helpful and the programs themselves easy to use. It is also an excellent reference and source of software for researchers and other practitioners who need computer solutions to differential equations.

Differential Equations. First Ideas and Single-Step Methods. Error Considerations. Runge-Kutta Methods. Step-Size Control. Dense Output. Stability and Stiffness. Multistep Methods. Multistep Formulae from Quadrature. Stability of Multistep Methods. Methods for Stiff Systems. Variable Coefficient Multistep Methods. Global Error Estimation. Second Order Equations. Partial Differential Equations. Appendix A: Programs for Single Step Methods. Appendix B: Multistep Programs. Appendix C: Programs for Stiff Systems. Appendix D: Global Embedding Programs. Appendix E: A Runge-Kutta Nyström Program. Bibliography. Index.