SOLUTION OF VOLTERRA-FREDHOLM INTEGRO-DIFFERENTIAL EQUATIONS USING CHEBYSHEV LEAST SQUARE METHOD

Abstract

This paper investigates the application of the least squares method for obtaining numerical solutions to Volterra-Fredholm integro-differential equations. The least squares method is a well-established approach for solving integral equations, and in this study, it is utilized to find approximate solutions to such equations. To enhance the accuracy of the solutions, Chebyshev polynomials are used as basis functions for the approximation process. These polynomials are chosen due to their favorable convergence properties and their ability to provide accurate approximations over a wide range of problems. Several examples are included in this study to demonstrate the effectiveness and reliability of the proposed method. The numerical results obtained using the least squares method with Chebyshev polynomial approximations are compared with exact solutions, showing excellent agreement. The outcomes of this study indicate that the method is both efficient and reliable for solving Volterra-Fredholm integro-differential equations, offering a robust approach for practical applications.