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In this article, an improved collocation method based on the Morgan-Voyce polynomials for the approximates solution of multi-pantograph equations is introduced. The method is ba sed upon the improvement of Morgan-Voyce polynomial soluti ns with the aid of the residual error function. First, the Morgan-Voyce collocation method is applied to the multi-pantograph equa tions and then Morgan-Voyce polynomial solutions are obtained. Second, a error problem is constructed by means of the residual error function and this error problem is solved by using the Morgan-Voyce collo cation method. By summing the Morgan-Voyce polynomial solu ti ns of the original problem and the error problem, we have the impro ved Morgan-Voyce polynomial solutions. When the exact solu ti n of problem is not known, the absolute error can then be approxim ately computed by the Morgan-Voyce polynomial solution of t he error problem. Numerical examples that the pertinent features of the method are presented. We have applied all of the numerica l computations on computer using a program written in MATLAB.

An improved Morgan-voyce collocation method for numerical solution of multi-pantograph equations