Convergence and stability in the numerical integration of ordinary differential equations
نویسندگان
چکیده
منابع مشابه
The numerical integration of ordinary differential equations
A reliable efficient general-purpose method for automatic digital computer integration of systems of ordinary differential equations is described. The method operates with the current values of the higher derivatives of a polynomial approximating the solution. It is thoroughly stable under all circumstances, incorporates automatic starting and automatic choice and revision of elementary interva...
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Subject headings: Multirate time stepping / Local time stepping / Ordinary differential equations / Stiff differential equations / Asymptotic stability / High-order Rosenbrock methods / Partitioned Runge-Kutta methods / Mono-tonicity / TVD / Stability / Convergence. Het onderzoek dat tot dit proefschrift heeft geleid werd mede mogelijk gemaakt door een Peter Paul Peterichbeurs –verstrekt door d...
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The organizing committee of this Congress has invited me to give a survey of a branch of numerical analysis which I consider important. The name "numerical analysis" is of recent origin; it first became part of the common mathematical usage when the Institute for Numerical Analysis was founded in Los Angeles about 14 years ago. Since then, the word has become associated with such diverse activi...
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Abstract. In this paper we derive a class of numerical integration formulas of a parallel type for ordinary differential equations. These formulas may be used simultaneously on a set of arithmetic processors to increase the integration speed. Conditions for the convergence of such formulas are formulated. Explicit examples for two and four processor cases are derived. Results of numerical exper...
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where y(x) denotes the solution of the differential equation. The idea is to use a quadrature formula to estimate the integral of (1). This requires knowledge of the integrand at specified arguments x¿ in (xo, -To + h)—hence we require the values of y(x) at these arguments. A numerical integration method may be used to estimate y(x) for the required arguments. In this way a numerical integratio...
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ژورنال
عنوان ژورنال: MATHEMATICA SCANDINAVICA
سال: 1956
ISSN: 1903-1807,0025-5521
DOI: 10.7146/math.scand.a-10454