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The RPS algorithm to handle a class of computational models arising in computer science


Nisrein Jamal Abu-Darwish


Vol. 17  No. 10  pp. 238-242


In this paper, we apply the residual power series technique to find out the solutions for second-order integro-differential equations (IDEs) system of Volterra type subject to given initial conditions. The new technique is effective and easy to use for solving linear and nonlinear IDEs without linearization, perturbation, or discretization. This approach provides the solutions in the form of a rapidly convergent series with easily computable components using symbolic computation software. The proposed technique obtains the Taylor expansions of the solutions and reproduces the exact solutions when the solutions are polynomials. The solutions obtained using the present method are tested by solving initial value problems of IDEs. Graphical results, tabulate data, and numerical comparisons are presented and discussed quantitatively to illustrate the solutions. Numerical results show the potentiality, the generality, and the superiority of our algorithm for solving such problems arising in computer science.