Multi-point Taylor approximations in one-dimensional linear boundary value problems

DOI10.1016/j.amc.2008.11.015zbMath1158.65051OpenAlexW2086444233MaRDI QIDQ1002311

Nico M. Temme, Ester Pérez Sinusía, José Luis López

Publication date: 25 February 2009

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

Full work available at URL: https://doi.org/10.1016/j.amc.2008.11.015

zbMATH Keywords

algorithmsnumerical examplesboundary value problemFrobenius methodpower series methodsecond order linear differential equationsmulti-point Taylor expansions

Mathematics Subject Classification ID

Numerical solution of boundary value problems involving ordinary differential equations (65L10)

Related Items (14)

Two-point Taylor expansions and one-dimensional boundary value problems ⋮ New series expansions of the Gauss hypergeometric function ⋮ New analytic representations of the hypergeometric functions \({}_{p+1}F_p\) ⋮ A new multiscale algorithm for solving second order boundary value problems ⋮ A new algorithm of boundary value problems based on improved wavelet basis and the reproducing kernel theory ⋮ Two-point Taylor approximations of the solutions of two-dimensional boundary value problems ⋮ The use of two-point Taylor expansions in singular one-dimensional boundary value problems I ⋮ A three-point Taylor algorithm for three-point boundary value problems ⋮ Changing variables in Taylor series with applications to PDEs ⋮ Convergence analysis and detection of singularities within a boundary meshless method based on Taylor series ⋮ New series expansions of the \(_3F_2\) function ⋮ Least‐square collocation and Lagrange multipliers forTaylor meshless method ⋮ Uniform convergent expansions of integral transforms ⋮ CONVERGENCE ORDER OF THE REPRODUCING KERNEL METHOD FOR SOLVING BOUNDARY VALUE PROBLEMS

Cites Work

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• Uniform asymptotics for the incomplete gamma functions starting from negative values of the parameters
• Taylor polynomial solutions of linear differential equations.
• Two‐Point Taylor Expansions of Analytic Functions
• On the Asymptotic and Numerical Solution of Linear Ordinary Differential Equations
• A method for the approximate solution of the second‐order linear differential equations in terms of Taylor polynomials
• A Taylor expansion approach for solving integral equations
• Multi-point Taylor expansions of analytic functions

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