Numerical solution of nonlinear Volterra–Fredholm integro-differential equations via direct method using triangular functions

Abstract

a b s t r a c tAn effective direct method to determine the numerical solution of the specific nonlinear Volterra-Fredholm integro-differential equations is proposed. The method is based on new vector forms for representation of triangular functions and its operational matrix. This approach needs no integration, so all calculations can be easily implemented. Some numerical examples are provided to illustrate the accuracy and computational efficiency of the method.

An efficient hybrid method for solving fredholm integral equations using triangular functions

“…In this section, definitions of vector forms of TFs vector forms and their properties proposed by Babolian et al [25] are reviewed.…”

Solution of Nonlinear Volterra-Fredholm Integrodifferential Equations via Hybrid of Block-Pulse Functions and Lagrange Interpolating Polynomials

“…As a concrete example, we can express the mathematical model of cell-to-cell spread of HIV-1 in tissue cultures considered by Mittler et al 6 . Yalcinbas and Sezer 7 proposed an approximation scheme based on Taylor polynomials for solving the high-order linear Volterra-Fredholm integrodifferential equations of the following form: 15 suggested an effective direct method to determine the numerical solution of the specific nonlinear Volterra-Fredholm integrodifferential equations. Their approach was based on triangular functions.…”

National economies in state-space of fractional-order financial system

“…Solution of nonlinear Volterra-Fredholm integral equations [8], Babolian et al have applied this method for solving nonlinear Volterra-Fredholm integro-differential equations [9], Maleknejad and Almasieh have applied via TFs for Optimal control of Volterra integral equations [10].…”