The discrete homotopy perturbation Sumudu transform method for solving partial difference equations

Abstract

In this paper, we introduce a combined form of the discrete Sumudu transform method with the discrete homotopy perturbation method to solve linear and nonlinear partial difference equations. This method is called the discrete homotopy perturbation Sumudu transform method(DHPSTM). The results reveal that the introduced method is very efficient, simple and can be applied to other linear and nonlinear difference equations. The nonlinear terms can be easily handled by use of He's polynomials.

A heuristic review on the homotopy perturbation method for non-conservative oscillators

“…43,44 The method was originally proposed to solving differential equations, but it can be used to solve fractal differential equations, 45,46 fractional differential equations, 47 and integral equations, 48,49 and difference equations. 50 It is extremely effective for inverse problems. [51][52][53] The strong motive for this work is to avoid errors and erroneous results that occur due to the use of the classical method for problems involving damping forces.…”

“…43,44 The method was originally proposed to solving differential equations, but it can be used to solve fractal differential equations, 45,46 fractional differential equations, 47 and integral equations, 48,49 and difference equations. 50 It is extremely effective for inverse problems. 51–53…”

Discrete Homotopy Analysis Method to Solve Nabla Fractional Partial Difference Equations

“…Recently there have been some results for nabla fractional difference equations [3,8,9,10]. Discovering a suitable method for solving partial difference equations has become important [11,12]. The discrete homotopy analysis method is the discretization of the homotopy analysis method proposed by Liao in 1992 [13].…”

A Transformation Method for Delta Partial Difference Equations on Discrete Time Scale

“…e qualitative analysis of delay partial difference equations is considered as discrete analog of delay partial differential equations by Zhang and Zhou [35]. For solving partial difference equations Ozpinar and Belgacem introduced discrete homotopy perturbation Sumudu transform method in [36]. For solving partial differential equations, double Laplace transform was applied in [37,38].…”