A numerical approach to the solution of nonlinear Volterra-Fredholm integro-differential equations

Abstract

In this study, a numerical method is presented for solving first-order Volterra-Fredholm Integro-differential Equations (V-FIDEs). The approach converts V-FIDEs into integral equations and uses power series polynomials to approximate them. The modeled problem is transformed into a system of algebraic equations, and then it is solved using the standard collocation method. Numerical examples are utilized to assess the method’s effectiveness after the approach’s uniqueness and convergence have been established. The results demonstrate that the method competes favorably with other methods.

Keywords

• collocation method
• volterra-fredholm
• integro-differential equations
• approximate solution
• polynomial power series