Two Numerical Methods to Solve the Second Order Multi-pantograph Equation with Boundary Conditions

Abstract

In this article, we present two numerical methods to solve the second order multi-pantograph equation with boundary conditions. The multi-pantograph equation is converted to an integral equation then the integral equation is solved by two projective methods. Some properties of Chebyshev polynomials are employed to prove the convergence analysis of the two proposed methods. Finally, numerical examples also are given to illustrate the efficiency and validity of the two proposed methods.