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

Since various problems in science and engineering fieldscan be modeled by nonlinear volterra-fredholm integral equations, themain focus of this study is to present an effective numerical method forsolving them. this method is based on the hybrid functions of legendrepolynomials and block-pulse functions. by using this approach, anonlinear volterra-fredholm integral equation reduces to a nonlinearsystem of mere algebraic equations. the convergence analysis and associatedtheorems are also considered. test problems are provided toillustrate its accuracy and computational efficiency.