A residual power series method for solving pseudo hyperbolic partial differential equations with nonlocal conditions

Abstract

This article will give the residual power series method (RPSM) for solving pseudo hyperbolic partial differential equations with nonlocal conditions, RPSM is essentially based on general formula of Taylor series with residual error function. A new analytical solution is investigated. The analytical solution is designed to find the approximation solutions by RPSM and compare the obtained results from the current method with the exact solution that detects the precision, reliability, and rapid convergence of the proposed method. Finally at different times through the graphical representation of obtained results are given.

Residual Power Series Method for Solving Klein-Gordon Schrödinger Equation

“…While, the reminder linear term is , the nonlinear operator is . Now, the solution of Equations (4) by RPSM around the initial point t=0 is written as a power series [1], [6], [8] and [9] as follow:…”

“…Then, the n-th residual function ) ( , ), ) ( , ) and ) ( , ) is defined as follow: 26) and ( 27) = 1,2,3, … .. and for equations (28) = 2,3, … [9]. Then, we will have :…”

“…(2013) to find the solution of generalized Lane-Emden equations in [1] and it has been applied in 2016 by İnç, M., Korpinar, Z. S., Al Qurashi, M. M., & Baleanu, D. to find the approximate solutions of some nonlinear equations [6]. It was also applied by Manaa, S. A.,& Mosa, N. M. in 2019 to solve the Kaup-Boussinesq System [8] and by Modanli, M., Abdulazeez, S. T., & Husien, A. M. in 2020 to solve "pseudo hyperbolic partial differential equations with nonlocal conditions" [9]. In this paper, the Residual Power Series Method (RPSM) [1], [6], [8] and [9] is applied to solve Klein-Gordon Schrödinger (KGS) Equation.…”

“…It was also applied by Manaa, S. A.,& Mosa, N. M. in 2019 to solve the Kaup-Boussinesq System [8] and by Modanli, M., Abdulazeez, S. T., & Husien, A. M. in 2020 to solve "pseudo hyperbolic partial differential equations with nonlocal conditions" [9]. In this paper, the Residual Power Series Method (RPSM) [1], [6], [8] and [9] is applied to solve Klein-Gordon Schrödinger (KGS) Equation. Moreover, we got all results and figures by using Mathematica program.…”

Exact solutions of the Benney–Luke equation via (1/G')-expansion method

“…(1 / ) G -expansion method [6][7][8][9] the Clarkson-Kruskal direct method [10], the auto-Bäcklund transformation method [11], decomposition method [12], homogeneous balance method [13], the first integral method [14], residual power series method [15], collocation method [16], modified Kudryashov method [17], sine-Gordon expansion method [18,19], the improved Bernoulli sub-equation function method, [20] and so on [21][22][23][30][31][32][33][34][35][36][37][38][39][40][41][42][43].…”