Multiple Perturbed Collocation Tau-method for Solving High Order Linear and Non-Linear Boundary Value Problems
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Date
2014
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Abstract
This paper is concerned with the numerical solution of high order linear and nonlinear boundary value problems of ordinary differential equations by Multiple Perturbed Collocation Tau Method (MPCTM). We assumed a perturbed apporoximate solution in terms of Chebyshev polynomial basis function which is subtituted into the special class of the problem considered. Thus, resulting into n-folds integration. After evaluation of n-fold integration, the resulting equation is then collocation at equally spaced interior points and the unknown constants in the approximate solution are then obtained by Gaussian elimination method which are then substituted back into the approximate solution. The proposed method is tested on several numerical examples, the approximate solution is in agreement with the exact solution. The approximate results obtained by the proposed method confirm the convergency of numerical solutions and are compared favourably with the existing methods available in literature.
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Keywords
Accuracy, Boundary Value Problems, Errors, Chebyshev, Collocation, Multiple Perturbed, Ordinary Differential Equation