In this paper, polynomial differential quadrature method (PDQM) is applied to find the numerical solution of generalized Fitzhugh–Nagumo equation with time-dependent coefficients in one dimensional space. The PDQM reduces problem into a system first order non-linear equations. Then, obtained solved by optimal four-stage, three strong stability-preserving time-stepping Runge–Kutta (SSP-RK43) scheme. accuracy and efficiency proposed are demonstrated test examples. results shown max absolute...

In this work, the variable-coefficient modified Burgers-KdV equation, which arises in modeling various physical phenomena, is studied for exact and numerical solution based on Lie symmetry. The infinitesimals of group transformations leaves equation invariant are furnished along with admissible forms variable coefficients. optimal systems one-dimensional subalgebras symmetry algebras determined adjoint action group. These then used to establish new power series solutions equation. Further,...

In this paper, a variable-coefficient Benjamin—Bona—Mahony—Burger (BBMB) equation arising as mathematical model of propagation small-amplitude long waves in nonlinear dispersive media is investigated. The integrability such an studied with Painlevé analysis. Lie symmetry method performed for the BBMB and then similarity reductions exact solutions are obtained based on optimal system method. Furthermore different types solitary, periodic kink can be seen change variable coefficients.

Purpose This paper aims to deal with two-dimensional magneto-hydrodynamic (MHD) Falkner–Skan boundary layer flow of an incompressible viscous electrically conducting fluid over a permeable wall in the presence magnetic field. Design/methodology/approach Using Lie group approach, algebra infinitesimal generators equivalence transformations is constructed for equation under consideration. these suitable similarity transformations, governing partial differential equations are reduced linear and...

Using the Lie symmetry approach, author has examined traveling wave solutions of coupled Benjamin–Bona–Mahony-KdV equation. The equation is reduced to nonlinear ordinary differential equations for all optimal subalgebras by using classical symmetries and various are obtained modified (G′/G)-expansion method. Further, with aid equations, more explicit found out. expressed rational function.

Abstract The current study is dedicated to solving the time-fractional (2+1)-dimensional Navier–Stokes model. model has wide applications in blood flow, design of power stations, weather prediction, ocean currents, water flow a pipe, air around aircraft wings, analysis pollution, and many other areas engineering. Lie symmetry approach applied governed equation fulfill this need. In direction exact solutions first all invariance condition obtained presence group. Consequently, infinitesimals...

The present study is carried out to examine the effects of magnetic field-dependent viscosity on steady axi-symmetric ferrofluid flow due rotating disk in porous medium. momentum equations give rise highly nonlinear partial differential equations, which are converted a system coupled ordinary using Karman's similarity transformation. Then numerical technique, combination finite difference and shooting methods, employed MATLAB environment get solution problem. Beside velocity pressure...

Purpose – The purpose of this paper is to propose a numerical technique based on polynomial differential quadrature method (PDQM) find the solutions two-space-dimensional quasilinear hyperbolic partial equations subject appropriate Dirichlet and Neumann boundary conditions. Design/methodology/approach PDQM reduced into system second order linear equation. obtained solved by RK4 converting first ordinary equations. Findings accuracy proposed demonstrated several test examples. results are...

The current work is devoted for operating the Lie symmetry approach, to coupled complex short pulse equation. method reduces equation a system of ordinary differential equations with help suitable similarity transformations. Consequently, these systems nonlinear under each subalgeras are solved traveling wave solutions. Further, variable, solutions and equation, soliton obtained which in form sinh, cosh, sin cos functions.

In this paper, the variable-coefficient diffusion—advection (DA) equation, which arises in modeling various physical phenomena, is studied by Lie symmetry approach. The similarity reductions are derived determining complete sets of point symmetries and then exact numerical solutions reported for reduced second-order nonlinear ordinary differential equations. Further, an extended (G'/G)-expansion method applied to DA equation construct some new non-traveling wave solutions.

The Lie symmetry analysis is performed for the coupled short plus (CSP) equation. We derive infinitesimals that admit classical group. Five types arise depending on nature of generator. In all types, we find reductions in terms system ordinary differential equations, and exact solutions CSP equation are derived, which compared with numerical using fourth-order Runge—Kutta scheme.

The current study is dedicated to the optical soliton solutions and modulation instability of Cubic–quartic Fokas–Lenells equation with nonlinear perturbation polarization-preserving fibers. In this direction, we take help Lie Symmetry analysis method. First all, obtained invariant condition which plays important role in mechanism symmetry After that, developed appropriate vector fields. Consequently, application these fields similarity are form trigonometric functions. Further, work,...

Purpose The aim of the present study is to examine ferrohydrodynamic laminar boundary layer flow electrically non-conducting magnetic fluid on a uniformly heated and radially stretchable disk with or without rotation in presence an externally applied field.

The purpose of present study is to investigate the effects field dependent viscosity on swirling flow an incompressible electrically non-conducting ferrofluid over a porous rotating disk with suction and heat transfer at wall. Karman's similarity transformations are used convert governing boundary layer equations involved in problem system nonlinear coupled differential equations. solution this obtained by using second-order numerical scheme which combines features Finite Difference method...

A theoretical analysis is made for a fully developed mixed convection viscous fluid flow between two infinite vertical parallel plane walls, where porous substrate of finite thickness attached to the left wall, in presence radiation and dissipation effects. It assumed that gray, absorbing-emitting but non-scattering medium. The Boussinesq approximation Rosseland are employed. analytic expressions temperature velocity profiles obtained effects permeability substrate, Grashof number,...

Abstract In this article, the authors apply Lie symmetry approach and modified $( G'/G )$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mo>(</mml:mo><mml:msup><mml:mi>G</mml:mi><mml:mo>′</mml:mo></mml:msup><mml:mo>/</mml:mo><mml:mi>G</mml:mi><mml:mo>)</mml:mo></mml:math> -expansion method for seeking solutions of time-dependent coupled KdV–Burgers equation. Using suitable similarity transformations, equation is reduced to a system nonlinear ordinary differential equations....

The hyperbolic nonlinear Schrödinger equation in the (3 + 1)‐dimension depicts evolution of elevation water wave surface for slowly modulated trains deep water. Many researchers have studied applicability and practicality this model, but analytical approach has been virtually absent from literature. We adapted lie symmetry analysis method to obtain a new complex solution work. obtained contains bright dark solitons. Furthermore, modulation instability is applied model explain interplay...

The current study is dedicated for operating the Lie symmetry approach, to complex short pulse equation. method reduces equation a system of ordinary differential equations with help suitable similarity transformations. Consequently, these systems nonlinear under each subalgebras are solved exact solutions. Further, variable, solutions and equation, soliton obtained which in form hyperbolic functions trigonometric functions.