A collocation method is proposed to obtain an approximate solution of a system of multi pantograph type delay differential equations with variable coefficients subject to the initial conditions. The general approach is that, first of all the solution of the system has been expanded according to First Boubaker polynomials (FBPs) basis. Then, by employing the matrix operations and collocation nodes, the original problem and the associated initial conditions are reduced to a nonlinear system. By solving such system, the unknown coefficients of the approximate solution can be determined. Convergence analysis of the proposed method has been proved. The presented method has been tested on three different examples. The computed results confirm the high accuracy of collocation method based on FBPs.
Numerical schemes have been developed for solutions of systems of nonlinear mixed Volterra-Fredholm integral equations of the second kind based on the First Boubaker polynomials (FBPs). The classical operational matrices are derived. The unknown has been approximated by FBPs and the Newton-Cotes points were applied as the collocations points. Error estimate and convergence analysis of the proposed method have been proved. Some numerical experiments are considered. The results are compared with relevant studies in order to test the reliability, validity and effectiveness of the proposed approach.
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