 Approximate solution of linear ordinary differential equations with variable coefficientsXian-Fang Li Mathematics and Computers in Simulation (MATCOM), 2007, vol. 75, issue 3, 113-125 Abstract: In this paper, a novel, simple yet efficient method is proposed to approximately solve linear ordinary differential equations (ODEs). Emphasis is put on second-order linear ODEs with variable coefficients. First, the ODE to be solved is transformed to either a Volterra integral equation or a Fredholm integral equation, depending on whether initial or boundary conditions are given. Then using Taylor’s expansion, two different approaches based on differentiation and integration methods are employed to reduce the resulting integral equations to a system of linear equations for the unknown and its derivatives. By solving the system, approximate solutions are determined. Moreover, an n th-order approximation is exact for a polynomial of degree less than or equal to n. This method can readily be implemented by symbolic computation. Illustrative examples are given to demonstrate the efficiency and high accuracy of the proposed method. Keywords: Approximate solution; Taylor’s expansion; Ordinary differential equations; Variable coefficient (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:75:y:2007:i:3:p:113-125 DOI: 10.1016/j.matcom.2006.09.006 Access Statistics for this article Mathematics and Computers in Simulation (MATCOM) is currently edited by Robert Beauwens More articles in Mathematics and Computers in Simulation (MATCOM) from Elsevier |
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