Differential transform method for solving singularly perturbed Volterra integral equations

Abstract

In this work, the applications of differential transform method were extended to singularly perturbed Volterra integral equations. To show the efficiency of the method, some singularly perturbed Volterra integral equations are solved as numerical examples. Numerical results show that the differential transform method is very effective and convenient for solving a large number of singularly perturbed problems with high accuracy.

A Numerical Method for Solving Singularly Perturbed Quasilinear Boundary Value Problems on Shishkin Mesh

“…Therefore, some important techniques have been introduced in the literature. These involve: finite difference methods [1,4,5,8,11,12,15], fitted mesh method [23], reproducing kernel method [7], factorization method [25], Galerkin method [18,26], differential transform method [9], variational iteration methods [2,10] and so on [6,16,19,20,27].…”

Solving three-dimensional Volterra integral equation by the reduced differential transform method

“…In literature, different methods have been used to solve one and two-dimensional Volterra integral equation see for example [2,7,10,11,14] and the references in [3,13]. In the recent years, many researchers studied Volterra integral equation using the differential transform method (DTM) [1,5,6,9]. For three-dimensional integral equations, in [4] the author used the three-dimensional differential transform method and authors in [8] applied the block-pulse functions methods on three-dimensional nonlinear mixed Volterra-Fredholm integral equation.…”

Modification Of High Performance Training Algorithms for Solve Singularly Perturbed Volterra integro-differential and integral equation

“…IN [2] have proposed the HPM for solving the SPVIEs, Alquran and Khair [3] solved the same problem by DTM and VIM. Finally, Dogan et al [4] used DTM to solve the presented problem. Liao [5], [6], [7] successfully applied the HAM to solve many types of nonlinear problems.…”