Fibonacci Wavelet Collocation Method for Solving a Class of System of Nonlinear Pantograph Differential Equations (Journal of Nonlinear Modeling and Analysis, 2025)
This paper introduces a unique strategy for solving numericallya class of nonlinear Pantograph differential equations using the Fibonacciwavelet collocation method (FWCM). First, we transform the nonlinear Pantograph differential equations system into a nonlinear algebraic system usingthis proposed approach. Next, the transformed nonlinear algebraic system issolved by using the Newton-Raphson scheme. The main advantage of thisapproach lies in its ability to reduce the computational complexity associatedwith solving Pantograph equations, resulting in accurate and efficient solutions. Comparative analyses with other established numerical methods revealits superior accuracy and convergence rate performance. Further, a few examples are provided to evaluate the effectiveness of the suggested approachusing absolute error functions. As far as our literature survey indicates, noone attempted the nonlinear Pantograph differential equations by FWCM. Itcompels us to study a system of Pantograph differential equations via FWCM.
Keywords: Pantograph equations; collocation technique; Fibonacci wavelet; operational matrix of integration.