A numerical approach with error estimation to solve general integro-differential-difference equations using Dickson polynomials
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Date
2016
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Abstract
In this paper, a matrix method based on the Dickson polynomials and collocation points is introduced for the numerical solution of linear integro-differential-difference equations with variable coefficients under the mixed conditions. In addition, in order to improve the numerical solution, an error analysis technique relating to residual functions is performed. Some linear and nonlinear numerical examples are given to illustrate the accuracy and applicability of the method. Eventually, the obtained results are discussed according to the parameter-α of Dickson polynomials and the residual error estimation. © 2015 Elsevier Inc. All rights reserved.
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Algorithms , Difference equations , Differential equations , Error analysis , Errors , Iterative methods , Matrix algebra , Numerical methods , Perturbation techniques , Analysis techniques , Dickson polynomial , Differential-difference equations , Homotopy Perturbation Method (HPM) , Matrix methods , Numerical approaches , Residual functions , Variable coefficients , Polynomials