Finite difference method with different high order approximations for solving complex equation

Abstract

Abstract:In this paper, we take finite difference method with different high order approximations for solving Hirota Equation is presented. The stability analysis using Von-Neumann technique shows schemes are unconditionally stable. To test accuracy the error norms L 2 , L ∞ are computed. We compute local truncation error for different schemes. We make comparison between these approximations through the results that we are get it. These results show that the approximation of O(k 2 + h 4 ) introduced here is more accurate than others and easy to apply.

Analytical and numerical study of the HIV‐1 infection of CD4+ T‐cells conformable fractional mathematical model that causes acquired immunodeficiency syndrome with the effect of antiviral drug therapy

“…In this section, we take approximations for t derivatives as follows 33‐35 : …”

“…[14][15][16][17][18][19] Recently, many researchers have addressed many of these phenomena through an analytical or numerical aspect. [20][21][22][23][24][25][26][27][28][29][30][31][32][33][34] In this sense, 2019-nCoV which the world suffers from such pandemic, has been investigated and studied deeply in numerical sense. [35][36][37][38][39][40][41] Moreover, COVID has affected almost all countries in economic, social, and psychological sense from all over the world.…”

“…There are many mathematical models that have applications in various fields such as engineering, physics, chemistry, and fluid mechanics to the last of these sciences 14‐19 . Recently, many researchers have addressed many of these phenomena through an analytical or numerical aspect 20‐34 . In this sense, 2019‐nCoV which the world suffers from such pandemic, has been investigated and studied deeply in numerical sense 35‐41 .…”

Electroosmosis forces EOF driven boundary layer flow for a non-Newtonian fluid with planktonic microorganism: Darcy Forchheimer model

“…The present study’s main target is to discuss the EOF on the boundary layer Williamson fluid model containing a gyrotactic microorganism through a Darcy–Forchheimer model flow in the presence of an electric and magnetic field. First, we discuss the details of the formulation of the problem, then describes the proposed solution methodology for the governing system of non-linear partial differential equations using the finite difference method (EL-Danaf et al , 2014; Raslan and Ali, 2020; Raslan et al , 2017; Ali et al , 2020), then prepare the numerical results and the significant results are discussed across all the leading parameters.…”

Exact Solution of Space-Time Fractional Coupled EW and Coupled MEW Equations Using Modified Kudryashov Method

“…The numerical solutions of nonlinear systems and nonlinear equations are very important in applied science, for example, the Hirota-Satsuma coupled KDV equation by Raslan et al [1] Also, the Hirota equation has been discussed by Raslan et al [2] The generalized long wave equation system has been studied by El-Danaf et al [3−4] The coupled-BBM system has been solved by Raslan et al [5−7] Coupled Burgers' Equations have been studied by Ali et al [8] and by Raslan et al [9] In the last years, many powerful and reliable methods have been proposed to obtain the exact solutions of fractional differential equations, such as first integral method, [10−15] ansatz method, [16−19] exp-function method, [20−24] functional variable method, [25−28] and Kudryashov method [29−30] have been proposed and utilized for extracting the exact solutions of fractional differential equations and so on.…”