in this paper, we present a comparative study between the modified variational iteration method (mvim) and a hybrid of fourier transform and variational iteration method (ftvim). the study outlines the efficiencyand convergence of the two methods. the analysis is illustrated by investigating four singular partial differential equations with variable coefficients. the solution of singular partia...

Abstract The aim of this work is to apply a semi-implicit (SI) strategy in an implicit-explicit (IMEX) Runge–Kutta (RK) setting introduced Boscarino et al. (J Sci Comput 68:975–1001, 2016) sequence 1D time-dependent partial differential equations (PDEs) with high order spatial derivatives. This gives great flexibility treat these equations, and allows the construction simple linearly implicit s...

we focus on the use of two stable and accurate explicit finite difference schemes in order to approximate the solution of stochastic partial differential equations of it¨o type, in particular, parabolic equations. the main properties of these deterministic difference methods, i.e., convergence, consistency, and stability, are separately developed for the stochastic cases.

A novel class of explicit high-order energy-preserving methods are proposed for general Hamiltonian partial differential equations with non-canonical structure matrix. When the energy is not quadratic, it firstly done that original system reformulated into an equivalent form a modified quadratic conservation law by quadratization approach. Then resulting satisfies discretized in time combining ...

In this paper, a collocation method for solving high-order linear partial differential equations (PDEs) with variable coefficients under more general form of conditions is presented. This method is based on the approximation of the truncated double exponential second kind Chebyshev (ESC) series. The definition of the partial derivative is presented and derived as new operational matrices of der...

Abstract We consider the construction of semi-implicit linear multistep methods that can be applied to time-dependent PDEs where separation scales in additive form, typically used implicit-explicit (IMEX) methods, is not possible. As shown Boscarino et al. (J. Sci. Comput. 68: 975–1001, 2016) for Runge-Kutta these techniques give a great flexibility, and allow, many cases, simple linearly impli...

At present, deep learning based methods are being employed to resolve the computational challenges of high-dimensional partial differential equations (PDEs). But computation high order derivatives neural networks is costly, and lack robustness for training purposes. We propose a novel approach solving PDEs with by simultaneously approximating function value derivatives. introduce intermediate v...

in this paper, the solution of the evolutionaryfourth-order in space, sivashinsky equation is obtained by meansof homotopy perturbation method (textbf{hpm}). the results revealthat the method is very effective, convenient  and quite accurateto systems of nonlinear partial differential equations.