The varying piecewise interpolation solution of the Cauchy problem for ordinary differential equations with iterative refinement

DOI10.1134/S0965542517100074zbMath1383.65072OpenAlexW2766590360MaRDI QIDQ1702621

Ya. E. Romm, G. A. Dzhanunts

Publication date: 28 February 2018

Published in: Computational Mathematics and Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s0965542517100074

zbMATH Keywords

computational complexityCauchy problemnumerical experimentsconvergence ratepiecewise interpolation approximationsanalog of Picard successive approximationsminimization of the approximation errornonstiff and stiff problems

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Stability and convergence of numerical methods for ordinary differential equations (65L20) Numerical methods for initial value problems involving ordinary differential equations (65L05) Error bounds for numerical methods for ordinary differential equations (65L70) Complexity and performance of numerical algorithms (65Y20) Numerical methods for stiff equations (65L04)

Related Items (1)

Variable piecewise interpolation solution of the transport equation

Uses Software

• RODAS

Cites Work

• The computer method of variable piecewise polynomial approximation of functions and solutions of ordinary differential equations
• Method for constructing approximate analytic solutions of differential equations with a polynomial right-hand side
• Sorting-based localization and stable computation of zeros of a polynomial. II.
• Klassische Runge-Kutta-Formeln fünfter und siebenter Ordnung mit Schrittweiten-Kontrolle
• Приближенное аналитическое решение систем обыкновенных дифференциальных уравнений с полиномиальной правой частью
• Solving Ordinary Differential Equations II
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