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Derivation of finite difference methods by interpolation and collocation. (English) Zbl 1302.65169

Summary: In this paper we derive finite difference methods by a power series form of multistep collocation for the solution of the initial value problems for ordinary differential equations. By selection of points for both interpolation and collocation, many important classes of finite difference methods are produced including new ones which are generally more accurate (smaller error constants) than the Adams-Moulton methods with adequate absolute stability intervals for a nonstiff problem.

MSC:

65L12 Finite difference and finite volume methods for ordinary differential equations
65L05 Numerical methods for initial value problems involving ordinary differential equations
65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations
65L20 Stability and convergence of numerical methods for ordinary differential equations
65L60 Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations
34A34 Nonlinear ordinary differential equations and systems
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