Implicit extension of Taylor series method with numerical derivatives for initial value problems

DOI10.1016/j.camwa.2005.08.017zbMath1092.65056OpenAlexW1998584541MaRDI QIDQ815250

E. Miletics, Gy. Molnárka

Publication date: 16 February 2006

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.camwa.2005.08.017

zbMATH Keywords

stabilityconsistencynumerical examplesinitial value problemscollocation methodsfinite differencesTaylor series methodadaptive error controlnumerical derivativesimplicit algorithmsimplementation aspects

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) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations (65L60) Error bounds for numerical methods for ordinary differential equations (65L70)

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Uses Software

• RODAS
• ATOMFT
• Taylor

Cites Work

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• Implicit single step methods by spline-like functions for solution of ordinary differential equations
• Consistency and stability for some nonnegativity-conserving methods
• ATOMFT: Solving ODEs and DAEs using Taylor series
• A Program for the Automatic Integration of Differential Equations using the Method of Taylor Series
• An efficient method for the numerical evaluation of partial derivatives of arbitrary order
• On the Schur component preconditioners