Numerical solution of nonlinear Volterra–Fredholm integro-differential equations

New computational method for solving some 2-dimensional nonlinear Volterra integro-differential equations

“…In this study, the basic ideas of the previous works [5,6] and [7] are developed and applied to the (2). Also, we extend the 2-DDTM to solve the 2-DNVIDE.…”

“…During the last 10 years, significant progress has been made in numerical analysis of one-dimensional version of (2) (see, [1][2][3][4] and in the references cited there). However, the numerical methods for two-dimensional integral and integro-differential equations seem to have been discussed in only a few places.…”

“…The technique that we used is the differential transform method, which is based on Taylor series expansion. Using the differential transform, (2) can be transformed to algebraic equations, and the resulting algebraic equations are called iterative equations. In order to solve the 2-DNVIDE by DTM it's basic theory is stated in Section 2.…”

Solving Nonlinear Volterra | Fredholm Integro-differential Equations Using the Modified Adomian Decomposition Method

“…(1.1) reduces to the following equation: Since many physical problems are modeled by integro-differential equations, the numerical solutions of such integro-differential equations have been highly studied by many authors. In recent years, numerous works have been focusing on the development of more advanced and efficient methods for integral equations and integro-differential equations such as the lineaziation method [1], the differential transform method [2], RF-pair method [3], and semianalytical-numerical techniques such as the Adomian decomposition method [5] and Taylor polynomials method [4,[6][7][8]. The modified decomposition method for solving nonlinear Volterra -Fredholm integral equations was presented by Bildik and Inc in [9].…”

Nonlinear Integro-differential Equations by Differential Transform Method with Adomian Polynomials

“…Nonlinear integral and integro-differential equations are usually hard to solve analytically and exact solutions are rather difficult to be obtained. In literature nonlinear integral and integro-differential equations can be solved by many numerical methods such as the Legendre wavelets method [4], the Haar functions method [5,6], the linearization method [7], the finite difference method [8], the Tau method [9,10], the hybrid Legendre polynomials and block-pulse functions [11], the Adomian decomposition method [12,13], the Taylor polynomial method [14][15][16] and the differential transform method [17].…”