×

zbMATH — the first resource for mathematics

Large amplitude instability in finite difference approximations to the Klein-Gordon equation. (English) Zbl 0937.65098
The author considers some finite difference approximations devised by S. Jiminez and L. Vazquez [Appl. Math. Comput. 35, No. 1, 61-94 (1990; Zbl 0691.65090)] for nonlinear Klein-Gordon equations. He analyzes the application of the schemes to a linear problem and suggests some alternative approximations. He develops conservation relations and obtains stability criteria by a von Neumann type analysis and suggests why some schemes are unstable. Two schemes are indicated which do not exhibit large amplitude stability.

MSC:
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
35Q53 KdV equations (Korteweg-de Vries equations)
PDF BibTeX XML Cite
Full Text: DOI