Extended two-dimensional DTM and its application on nonlinear PDEs with proportional delay

Homotopy perturbation transform method for solving fractional partial differential equations with proportional delay

“…To best of my knowledge, a little literature of numerical techniques to solve TFPDE with delay, among them, Chebyshev pseudospectral method for linear differential and differentialfunctional parabolic equations by Zubik-Kowal [37], spectral collocation & waveform relaxation methods by Zubik-Kowal and Jackiewicz [38] and iterated pseudospectral method [39] for nonlinear delay partial differential equations, two dimensional differential transform method (2D-DTM) and RDTM for partial differential equations with proportional delay by Abazari and Ganji [40], Abazari and Kilicman [41] used DTM for nonlinear integro-differential equations with proportional delay, group analysis method for nonhomogeneous mucilaginous Burgers equation with proportional delay due to Tanthanuch [42], homotopy perturbation method for TFPDE with proportional delay by Sakar et al [34] and Shakeri-Dehghan [43], and Biazar ad Ghanbari [44], variational iteration method (VIM) for solving a neutral functional-differential equation with proportional delays by Chena and Wang [45], functional constraints method for the exact solutions of nonlinear delay reaction-diffusion equations by Polyanin and Zhurov [46], and so on.…”

A computational modelling of micro strip patch antenna and its solution by RDTM

“…Definition 3.1. If wðx; tÞ is analytic and continuously differentiable with respect to space variable x and time variable t in the domain of interest, then the spectrum function [3][4][5] R D ½wðx; tÞ % W k ðxÞ ¼ 1 k! @ k @t k wðx; tÞ…”

“…The differential inverse reduced transform of W k ðxÞ is defined as [3][4][5] R À1 D ½W k ðxÞ % wðx; tÞ ¼…”

“…In this section, the fundamental of the reduced differential transformation is described [3][4][5][6][7][8][9][10][11]. Consider a function of two variables wðx; tÞ, and assume that it can be represented as a product of two single-variable functions, i.e.…”

Application of Differential Transformation Method for Numerical Computation of Regularized LongWave Equation

“…Borhanifar and Abazari applied this method for the Schrödinger equation [17]. Authors of [18,19] used it for an approximate solution of the Hantavirus infection model and Emden-Fowler type differential equations.…”