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Asymptotic analysis of finite difference methods. (English) Zbl 1061.65084
Summary: We want to advocate the use of asymptotic methods for the analysis of finite difference schemes. We present several examples to demonstrate the applicability of the approach. Advantages over the modified equation and truncation error analysis are pointed out.

MSC:
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
34A34 Nonlinear ordinary differential equations and systems, general theory
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
65L70 Error bounds for numerical methods for ordinary differential equations
65L12 Finite difference and finite volume methods for ordinary differential equations
65L05 Numerical methods for initial value problems
35L45 Initial value problems for first-order hyperbolic systems
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