Application of Legendre wavelet method coupled with the Gauss quadrature rule for solving fractional integro-differential equations

Document Type : Original Paper


Department of Mathematics, Higher Education Complex of Saravan, Saravan, Iran


In this work, we propose a novel technique for solving the nonlinear fractional Volterra-Fredholm integro-differential equations (FVFIDEs). This method approximates the unknown function with the Legendre wavelets. To do this, the Legendre wavelets are used in conjunction with the quadrature rule for converting the problem into a linear or nonlinear system of algebraic equations which can be easily solved by applying the mathematical programming techniques. Furthermore, the existence and uniqueness of the solution are proved by preparing some theorems and lemmas. Also, the error estimate and convergence analysis of the method will be shown. Moreover, some examples are presented and their results are compared to the results of Chebyshev wavelet, modification of hat functions, NystrÖm and Newton-Kantorovitch methods to show the capability and accuracy of this scheme.


Main Subjects

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