Abstract: In this work, we successfully extended one-dimensional differential transform method (DTM), by presenting and proving some theorems, to solving nonlinear high-order multi-pantograph equations. This technique provides a sequence of functions which converges to the exact solution of the problem. Some examples are given to demonstrate the validity and applicability of the present method and a comparison is made with existing results.
Abstract: In this work we adopt a combination of Laplace
transform and the decomposition method to find numerical solutions
of a system of multi-pantograph equations. The procedure leads to a
rapid convergence of the series to the exact solution after computing a
few terms. The effectiveness of the method is demonstrated in some
examples by obtaining the exact solution and in others by computing
the absolute error which decreases as the number of terms of the series
increases.