A numerical method for solving some model problems arising in science and convergence analysis based on residual function
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Date
2017
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Abstract
In this study, we solve some widely-used model problems consisting of linear, nonlinear differential and integral equations, employing Dickson polynomials with the parameter-α and the collocation points for an efficient matrix method. The convergence of a Dickson polynomial solution of the model problem is investigated by means of the residual function. We encode useful computer programs for model problems, in order to obtain the precise Dickson polynomial solutions. These solutions are plotted along with the exact solutions in figures and the numerical results are compared with other well-known methods in tables. © 2017 IMACS
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Keywords
Convergence of numerical methods , Integral equations , Nonlinear equations , Numerical methods , Problem solving , Collocation points , Convergence , Convergence analysis , Dickson polynomial , Matrix methods , Nonlinear differential and integral equations , Numerical results , Residual functions , Polynomials