Purpose – The purpose of this paper is to use the polynomial differential quadrature method (PDQM) to find the numerical solutions of some Burgers’-type nonlinear partial differential equations. Design/methodology/approach – The PDQM changed the nonlinear partial differential equations into a system of nonlinear ordinary differential equations (ODEs). The obtained system of ODEs is solved by Ru...

The flow of an incompressible electrically conducting viscous fluid in convergent or divergent channels under the influence of an externally applied homogeneous magnetic field is studied both analytically and numerically. Navier-Stokes equations of fluid mechanics and Maxwell’s electromagnetism equations are reduced into highly non-linear ordinary differential equation. The resulting non-linear...

In this paper, we analyze the stability of the fourth order Runge-Kutta method for integrating semi-discrete approximations of time-dependent partial differential equations. Our study focuses on linear problems and covers general semi-bounded spatial discretizations. A counter example is given to show that the classical four-stage fourth order Runge-Kutta method can not preserve the one-step st...

In this paper, a fractional order HIV/AIDS (FOHA) epidemic model with treatment is investigated. The first step in the proposed procedure is represent the FOHA system as an equivalent system of ordinary differential equations. In the second step, we solved the system obtained in the first step by using the well known fourth order Runge-Kutta method. Numerical simulations are also presented to v...

Acoustic waves in a rigid axisymmetric tube with a variable cross-section are considered. The governing Helmholtz equation is solved using Neumann series (expansions in Bessel functions of various orders) with a stretched radial coordinate, leading to a hierarchy of one-dimensional ordinary differential equations in the longitudinal direction. The lowest approximation for axisymmetric motion in...

The governing equations for the unsteady flow of a uniformly conducting incompressible fourth-grade fluid due to noncoaxial rotations of a porous disk and the fluid at infinity are constructed. The steady flow of the fourth-grade fluid subjected to a magnetic field with suction/blowing through the disk is studied. The nonlinear ordinary differential equations resulting from the balance of momen...