A Projection Method for Solving Nonlinear Volterra-Fredholm Integral Equations using Legendre Hybrid Functions

Since various problems in science and engineering fields can be modeled by nonlinear Volterra-Fredholm integral equations, the main focus of this study is to present an effective numerical method for solving them. This method is based on the hybrid functions of Legendre polynomials and block-pulse functions. By using this approach, a nonlinear Volterra-Fredholm integral equation reduces to a nonlinear system of mere algebraic equations. The convergence analysis and associated theorems are also considered. Test problems are provided to illustrate its accuracy and computational efficiency.