An efficient method based on lucas polynomials for solving high-order linear boundary value problems
No Thumbnail Available
Date
2015
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Abstract
In this paper, a collocation method based on Lucas polynomials for solving high-order linear differential equations with variable coefficients under the boundary conditions is presented by transforming the problem into a system of linear algebraic equations with Lucas coefficients. The proposed approach is applied to fourth, fifth, sixth and eighth-order two-point boundary values problems occurring in science and engineering, and compared by existing methods. The technique gives better approximations than other methods, and has a lower computational cost. In addition, the error analysis based on residual function is developed for the present method and the improved approximate solution is obtained. Moreover, numerical examples are included to illustrate the practical usefulness and efficiency of the method. © 2015, Gazi University Eti Mahallesi. All rights reserved.
Description
Keywords
Boundary conditions , Error analysis , Linear algebra , Linear equations , Numerical methods , Polynomials , Boundary-value problem , Collocation method , High-order , Higher-order , Higher-order differential equation , Linear boundary value problem , Linear differential equation , Luca polynomial , Residual error analysis , Variable coefficients , Boundary value problems