Frobenius-Chebyshev polynomial approximations with a priori error bounds for nonlinear initial value differential problems

DOI10.1016/S0898-1221(00)00271-6zbMath1001.65073MaRDI QIDQ5948705

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Publication date: 12 November 2001

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

zbMATH Keywords

numerical resultsChebyshev polynomialsinitial value problema priori error boundFrobenius

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Numerical methods for initial value problems involving ordinary differential equations (65L05) Error bounds for numerical methods for ordinary differential equations (65L70)

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Chebyshev rational matrix approximation with a priori error bounds for linear and Riccati matrix equations ⋮ Regarding polynomial approximation for ordinary differential equations ⋮ Numerical solution for diffusion equations with distributed order in time using a Chebyshev collocation method ⋮ Explicit a-priori error bounds and adaptive error control for approximation of nonlinear initial value differential systems ⋮ Constructing accurate polynomial approximations for nonlinear differential initial value problems ⋮ Chebyshev polynomial approximations for nonlinear differential initial value problems ⋮ Chebyshev polynomial approximation for high‐order partial differential equations with complicated conditions ⋮ Numerical solution of hyperbolic telegraph equation using the Chebyshev tau method ⋮ The truncation error of the two-variable Chebyshev series expansions ⋮ Polynomial approximate solutions with a priori error bounds of first-order quasi-linear initial-value partial differential problems

Cites Work

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• Constructive polynomial approximation with \textit{a priori} error bounds for nonlinear initial value differential problems
• Numerical solution of multi-point boundary value problems in Chebyshev series. Theorie of the method
• Orthogonal polynomials in two variables
• Applications of analysis on nilpotent groups to partial differential equations