A novel approach for numerical treatment of traveling wave solution of ion acoustic waves as a fractional nonlinear evolution equation on Shehu transform environment

Abstract

In this paper, we develop and employ an efficient numerical technique for traveling wave solution of the Time Fractional Zakharov-Kuznetsov (TFZK) equation, also known as the nonlinear evolution equation, using the Modified Adomian Decomposition Approach (MADA) in collaboration with the cubic order convergence of the Newton-Raphson method (also known as the improvised Newton-Raphson method) on the Shehu Transform environment (STE). In the current study, the time fractional Caputo-Fabrizio Derivative (CFD) is used in singular and non-singular kernel derivatives to address the influence of fractional parameters. Some of the current numerical and analytical results are displayed utilizing 3D plots, while others are depicted in the form of a legend 2D plots for comparison. To validate the robustness of the current approach, the uniqueness, stability, and convergence analyses are described. The current result is compared to the analytical solution as well as previous solutions in order to demonstrate the efficiency of our suggested technique.

The kink-antikink single waves in dispersion systems by generalized PHI-four equation in mathematical physics

“…For instances, recently LADT has been successfully implemented in a variety of differential model like; SDIQR model of Covid-19 [18], Lane emden differential equation [19], model of lassa diseases [20], numerical solution of large deflection beam [21], simulation of unsteady MHD flow in incompressible fluid [22], approximation of time fractional advection dispersion equation [23], approximate solution of fractional order sterile insect technology model [24] etc. Similarly various integral transforms [25,26] are implemented to solve higher order partial differential equations. Also various new soliton solution approaches are investigated; like Sardar sub-equation technique [27], multi soliton solution of Vakhnenko-Parkes equation [28], Coke price prediction approach [29], multivariate stochastic volatility models by using optimization mechanisms [30], Galilean transformation of Schrodinger equation [31], bifurcation analysis of Hindmarsh-Rose model [32] etc B-spline collocation [33][34][35] and the block method [36,37] are additional techniques that improve the current article and are advantageous to the existing system.…”

Explicit and Implicit Numerical Investigationof One-Dimensional Heat Equation Based on Spline Collocation and Thomas Algorithm

“…Integral boundary conditions with finite difference scheme [8,9]and cubic Hermite B-spline techniques [10]are used to solve the heat equation. The methods based on B-spline collocation technique [13][14][15][16][17][18][19][20][21][22][23][24][25][26][27] are beneficial to the present manuscript. The highlights of the present topic is the application of spline collocation method approach, to obtain approximate solution to one dimensional parabolic equation on explicit and implicit version.…”

A reliable method for voltage of telegraph equation in one and two space variables in electrical transmission: approximate and analytical approach

“…B-spline collocation for nonlinear partial differential equations by Jena and Gebremedhin [31][32][33][34], numerical solitons in B-spline environment by Jena et al [35,36] and Generalized Rosenau-RLW equation in B-spline scheme via BFRK approach by Senapati and Jena [37,38] have played a vital role towards this manuscript. The SDIQR mathematical modelling for Covid-19 of Odisha based on Laplace Adomian decomposition method is employed by Sahu and Jena [30] and Jena and Sahu [58] solved the fractional nonlinear evolution equation by using Shehu transform. Laplace decomposition method is also employed to solve nonlinear Kompaneets equation by González-Gaxiola et al [11] and nonlinear Klein-Gordon equation by Emad et al [13].…”