A Lie group integrator to solve the hydromagnetic stagnation point flow of a second grade fluid over a stretching sheet

Abstract

<abstract><p>In the present paper, a Lie-group integrator, based on $ GL(4, \mathbb{R}) $ has been newly constructed to consider the flow characteristics in an electrically conducting second grade fluid over a stretching sheet. Present method which have a very fast convergence, permits us to explore some missing initial values at the left-end. Accurate initial values can be achieved when the determined target equation is valid, and then we can apply the group preserving scheme (GPS) as a geometric approach to obtain a rather accurate numerical solution. Finally, effects of magnetic parameter, viscoelastic parameter, stagnation point flow and stretching of the sheet parameters are illustrated.</p></abstract>

A view of solitary wave solutions to the fractional DNA Peyrard-Bishop equation via a new approach

“…In this section, the approach briefly described above will be utilized for creating solitary wave solutions for the fractional DPB dynamic model equation. Let's consider equation ( 5) and equation (6). By applying the traveling wave transformation to these equations as follows,…”

“…Many researchers have thoroughly examined nonlinear partial differential equations (PDEs), and numerous techniques have been devised to address these PDEs. To obtain exact solutions to the nonlinear PDEs, various effective mathematical approaches have been utilized in the literature [1][2][3][4][5][6][7][8][9][10][11][12][13][14].…”

Analysis and soliton solutions of biofilm model by new extended direct algebraic method

“…In this modern era of research, finding soliton solutions is an important field to describe the physical behavior of the nonlinear PDEs. There are many different techniques to find the soliton solutions such as G /G expansion method https://www.journals.vu.lt/nonlinear-analysis [4,31], first integral method [5], Kudryashov method [3,8], generalized logistic equation method [22,34], Riccati mapping method [2,33], φ 6 -model expansion method [27,35], He's variational method [20], generalized exponential rational function method [12], Hirota bilinear method [11], modified exponential rational functional method [1], a new auxiliary equation [28], Riccati-Bernoulli sub-ODE method [7,16,19], etc. But in this study, we apply the new modified extended direct algebraic method and the existence of the solutions on the bistable Allen-Cahn equation with quartic potential.…”

A variety of new soliton structures and various dynamical behaviors of a discrete electrical lattice with nonlinear dispersion via variety of analytical architectures

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“…Other important studies have been performed in previous studies. 36,37 Fractional Brusselator reaction-diffusion 38 system arising in chemical reactions has been solved by a novel fractional reduced differential transform method. Togueu et al 38 recently examined a supratransmission phenomena in a discrete electrical lattice with nonlinear dispersion and showed that the nonlinear Salerno equation can be constructed and solutions found under certain parameters in upper and lower forbidden band gaps.…”