In this study, we aim to construct a traveling wave solution for nonlinear partial differential equations. In this regards, a cosine-function method is used to find and generate the exact solutions for three different types of nonlinear partial differential equations such as general regularized long wave equation (GRLW), general Korteweg-de Vries equation (GKDV) and general equal width wave equ...

One-dimensional parabolic equation; Nonlocal boundary conditions; Taylor approximation; Operational matrices; Krylov subspace iterative methods; Restarted GMRES Abstract This article contributes a matrix approach by using Taylor approximation to obtain the numerical solution of one-dimensional time-dependent parabolic partial differential equations (PDEs) subject to nonlocal boundary integral c...

We consider the numerical solution of a nonlocal partial differential equation which describes phenomenon collective spontaneous emission in two-level atomic system containing single photon. reformulate problem as an integro-differential for degrees freedom, and describe efficient solver case Gaussian density. The history dependence arising from integral formulation is addressed using sum-of-ex...

In this study, differential transform method (DTM) is applied to fuzzy integro-differential equation. The concept of generalized Hdifferentiability is used. If the equation has a solution in terms of the series expansion of known functions; this powerful method catches the exact solution. Some numerical examples are also given to illustrate the superiority of the method. All rights reserved.

In this paper, we present Legendre wavelet method to obtain numerical solution of a singular integro-differential equation. The singularity is assumed to be of the Cauchy type. The numerical results obtained by the present method compare favorably with those obtained by various Galerkin methods earlier in the literature.

This paper studies the uniqueness of bounded solution to a new Cauchy problem fractional nonlinear partial integro-differential equation based on multivariate Mittag–Leffler function as well Banach’s contractive principle in complete space. Applying Babenko’s approach, we convert with variable coefficients an implicit integral equation, which is powerful method studying solutions. Furthermore, ...