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On numerical integration of implicit ordinary differential equations

Z. Jackiewicz, M. Kwapisz

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Abstract

In this paper it is shown how the numerical methods for ordinary differential equations can be adapted to implicit ordinary differential equations. The resulting methods are of the same order as the corresponding methods for ordinary differential equations. The convergence theorem is proved and some numerical examples are given.

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What this paper is about

In this paper it is shown how the numerical methods for ordinary differential equations can be adapted to implicit ordinary differential equations. The resulting methods are of the same order as the corresponding methods for ordinary differential equations. The convergence theorem is proved and some numerical examples are given.

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OpenAlex reports 4 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

In this paper it is shown how the numerical methods for ordinary differential equations can be adapted to implicit ordinary differential equations. The resulting methods are of the same order as the corresponding methods for ordinary differential equations. The convergence theorem is proved and some numerical examples are given.

Key concepts: Mathematics, Explicit and implicit methods, Numerical methods for ordinary differential equations, Ordinary differential equation, Exponential integrator, Backward differentiation formula, Numerical partial differential equations, Differential algebraic equation

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