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

Masood Roodaki, Zahra JafariBehbahani JafariBehbahani

Abstract


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.

Keywords


Hybrid functions, nonlinear Volterra-Fredholm integral equations of the second kind, legendre polynomials, blockpulse functions, function expansion, cross product, coefficients matrix, projection method.

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