Lucas polynomial approach for system of high-order linear differential equations and residual error estimation
type: Item
instance of: scholarly article
title: Lucas polynomial approach for system of high-order linear differential equations and residual error estimation
zbMATH Open document ID: 1394.65061
DOI: 10.1155/2015/625984
author: Muhammed Çetin
author: Mehmet Sezer
author: Coskun Guler
published in: Mathematical Problems in Engineering
publication date: 2018-08-27T00:00:00Z
review text: Summary: An approximation method based on Lucas polynomials is presented for the solution of the system of high-order linear differential equations with variable coefficients under the mixed conditions. This method transforms the system of ordinary differential equations (ODEs) to the linear algebraic equations system by expanding the approximate solutions in terms of the Lucas polynomials with unknown coefficients and by using the matrix operations and collocation points. In addition, the error analysis based on residual function is developed for present method. To demonstrate the efficiency and accuracy of the method, numerical examples are given with the help of computer programmes written in \textit{Maple} and \textit{Matlab}.
Mathematics Subject Classification ID: 65L60
zbMATH DE Number: 6926834
Wikidata QID: Q59119157
describes a project that uses: Mathematica
describes a project that uses: Maple
describes a project that uses: Matlab
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2015/625984
OpenAlex ID: W2089448982
cites work: Improvement of He's variational iteration method for solving systems of differential equations
cites work: The numerical solutions of differential transform method and the Laplace transform method for a system of differential equations
cites work: Application to differential transformation method for solving systems of differential equations
cites work: The differential transform approximation for the system of ordinary differential equations
cites work: Solutions of the system of differential equations by differential transform method
cites work: Revised Adomian decomposition method for solving systems of ordinary and fractional differential equations
cites work: Solution of the system of ordinary differential equations by Adomian decomposition method.
cites work: Conditional linearizability criteria for a system of third-order ordinary differential equations
cites work: Linearization criteria for a system of second-order ordinary differential equations
cites work: Chebyshev finite difference method for a nonlinear system of second-order boundary value problems
cites work: The solution of linear and nonlinear systems of Volterra functional equations using Adomian-Padé technique
cites work: Chebyshev polynomial solutions of systems of high-order linear differential equations with variable coefficients
cites work: Bernstein series solutions of pantograph equations using polynomial interpolation
cites work: A collocation method using Hermite polynomials for approximate solution of pantograph equations
cites work: A numerical approach for solving initial-boundary value problem describing the process of cooling of a semi-infinite body by radiation
cites work: Comparison of Legendre polynomial approximation and variational iteration method for the solutions of general linear Fredholm integro-differential equations
cites work: Laguerre approach for solving pantograph-type Volterra integro-differential equations
cites work: An efficient algorithm for solving multi-pantograph equation systems
cites work: The solution of the Bagley-Torvik equation with the generalized Taylor collocation method
cites work: Taylor polynomial solution of high-order nonlinear Volterra-Fredholm integro-differential equations
cites work: Collocation and residual correction
cites work: Approximate calculation of eigenvalues with the method of weighted residuals-collocation method
cites work: Collocation method and residual correction using Chebyshev series
cites work: Numerical solution of the general form linear Fredholm-Volterra integro-differential equations by the tau method with an error estimation
cites work: Lucas polynomials and a standard Lax representation for the polytropic gas dynamics
cites work: Q4203611
cites work: Fibonacci and Lucas numbers with applications. Volume I
cites work: Application of He's homotopy perturbation method for non-linear system of second-order boundary value problems
description: scientific article; zbMATH DE number 6926834