Initial Value Problems
| Autor: | John A. Trangenstein |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Constant coefficients
Numerical analysis 010102 general mathematics Stability (learning theory) 010103 numerical & computational mathematics 01 natural sciences Mathematics::Numerical Analysis Matrix (mathematics) Ordinary differential equation Initial value problem Applied mathematics Uniqueness 0101 mathematics Mathematics Linear multistep method |
| Zdroj: | Texts in Computational Science and Engineering ISBN: 9783319691091 |
| DOI: | 10.1007/978-3-319-69110-7_3 |
| Popis: | This chapter is devoted to initial values problems for ordinary differential equations. It discusses theory for existence, uniqueness and continuous dependence on the data of the problem. Special techniques for linear ordinary differential equations with constant coefficients are discussed in terms of matrix exponentials and their approximations. Next, linear multistep methods are introduced and analyzed, leading to a presentation of important families of linear multistep methods and their stability. These methods are implemented through predictor-corrector methods, and techniques for automatically selecting stepsize and order are discussed. Afterwards, deferred correction and Runge-Kutta methods are examined. The chapter ends with the selection of numerical methods for stiff problems, and a discussion of nonlinear stability. |
| Databáze: | OpenAIRE |
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