The application of Least Squares Method and Shifted Chebychev Polynomials for solving fourth order Volterra Integro-Differential Equations

Abstract

This study employs the least squares method in conjunction with shifted Chebyshev polynomials as a framework to approximate solutions for fourth-order Volterra integro-differential equations. By leveraging this numerical approach, the method effectively tackles various fourth-order Volterra integro-differential equations, yielding results closely aligned with exact solutions. The utilization of the least squares method with shifted Chebyshev polynomials demonstrates its efficacy in solving such equations with exact and converges faster than existing methods. The tables and graphical representation below display this