Fibonacci Wavelet Collocation Method for Solving a Class of System of Nonlinear Pantograph Differential Equations

Abstract

This paper introduces a unique strategy for solving numerically a class of nonlinear Pantograph differential equations using the Fibonacci wavelet collocation method (FWCM). First, we transform the nonlinear Pantograph differential equations system into a nonlinear algebraic system using this proposed approach. Next, the transformed nonlinear algebraic system is solved by using the Newton-Raphson scheme. The main advantage of this approach lies in its ability to reduce the computational complexity associated with solving Pantograph equations, resulting in accurate and efficient solutions. Comparative analyses with other established numerical methods reveal its superior accuracy and convergence rate performance. Further, a few examples are provided to evaluate the effectiveness of the suggested approach using absolute error functions. As far as our literature survey indicates, no one attempted the nonlinear Pantograph differential equations by FWCM. It compels us to study a system of Pantograph differential equations via FWCM.