Variable-stepsize Chebyshev-type methods for the integration of second-order I.V.P.'s

DOI10.1016/j.cam.2006.04.032zbMath1117.65106OpenAlexW2053866204MaRDI QIDQ879415

Jesus Vigo Aguiar, Higinio Ramos

Publication date: 11 May 2007

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2006.04.032

zbMATH Keywords

numerical examplesinitial value problemssecond-order ordinary differential equationsvariable stepsizeChebyshev methods

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Numerical methods for initial value problems involving ordinary differential equations (65L05) Mesh generation, refinement, and adaptive methods for ordinary differential equations (65L50)

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Cites Work

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• Variable stepsize Störmer-Cowell methods
• A family of implicit Chebyshev methods for the numerical integration of second-order differential equations
• A family of embedded Runge-Kutta formulae
• The role of orthogonal polynomials in numerical ordinary differential equations
• Analysis of a family of Chebyshev methods for \(y=f(x,y)\)
• Dissipative Chebyshev exponential-fitted methods for numerical solution of second-order differential equations.
• Modification of the Richardson-Panovsky methods for precise integration of satellite orbits.
• New quadrature formulas based on the zeros of the Chebyshev polynomials of the second kind
• A Chebyshev expansion method for solving nonlinear optimal control problems.
• Stabilization of Cowell's method
• The solution of nonlinear ordinary differential equations in Chebyshev series
• Computing Zeros on a Real Interval through Chebyshev Expansion and Polynomial Rootfinding
• EXPONENTIALLY AND TRIGONOMETRICALLY FITTED EXPLICIT ADVANCED STEP-POINT (EAS) METHODS FOR INITIAL VALUE PROBLEMS WITH OSCILLATING SOLUTIONS