A Symbolic Method for Finding Approximate Solution of Neutral Functional-Differential Equations with Proportional Delays

Abstract

This paper presents a new symbolic method for finding an approximate solution of neutral functional-differential equations with proportional delays having variable coefficients in an algebraic setting. In several cases exact solution is obtained. This method is easy to apply for solving the multi-pantograph equations with variable coefficients. We introduce iterative operator. In the proposed method, the given problem is transformed into an operator based notation and again the solution of operator problem is translated into the solution of the given problem. The Maple implementation of the proposed algorithm is presented with sample computations. Various numerical examples are discussed to illustrate the efficiency of the proposed method, and comparisons are made to confirm the reliability of the method.

Key words and phrases. Differential operators, Integral operators, Successive approximations, Multi-pantograph equations, Neutral functional-differential equation.

2010 Mathematics Subject Classification. 65L05; 40A25; 41A10