A Galerkin-Like Approach to Solve Multi-Pantograph Type Delay Differential Equations

Abstract

In this paper, a Galerkin-like approach is presented to numerically
solve multi-pantograph type delay differential equations. The method
includes taking inner product of a set of monomials with a vector obtained
from the equation under consideration. The resulting linear system is then
solved, yielding a polynomial as the approximate solution. Also we give
an error analysis and the technique of residual correction, which aims to
increase the accuracy of the approximate solution. Lastly, the method,
error analysis and the residual correction technique are illustrated with
several examples. The results are also compared with numerous existing
methods from the literature.