Multiple Perturbed Collocation Tau Method for Solving Nonlinear Integro-Differential Equations
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Date
2019-01
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Faculty of Science, University of Port Harcout, Nigeria.
Abstract
: The purpose of the study was to investigate the numerical solution of non-linear Fredholm and Volterra
integro-differential equations by the proposed method called Multiple Perturbed Collocation Tau Method (MPCTM). We
assumed a perturbed approximate solution in terms of Chebyshev polynomial basis function and then determined the
derivatives of the perturbed approximate solution which are then substituted into the special classes of the problems
considered. Thus, resulting into n-folds integration, the resulting equation is then collocated at equally spaced interior
points and the unknown constants in the approximate solution are then obtained by Newton’s method which are then
substituted back into the approximate solution. Illustrative examples are given to demonstrate the efficiency,
computational cost and accuracy of the method. The results obtained with some numerical examples are compared
favourable with some existing numerical methods in literature and with the exact solutions where they are known in closed
form.
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Nonlinear Problems, Tau Method, Integro-Differential, Newton’s method.