A B-spline finite element method is used to solve the equal width equation numerically. This approach involves a collocation method using quintic B-splines at the knot points as element shape. Time integration of the resulting system of ordinary differential equations is effected using the fourth order Runge–Kutta method, instead of the finite difference method, the resulting system of ordinary...

The aim of this article is to model and analyze an unsteady axisymmetric flow of non-conducting, Newtonian fluid squeezed between two circular plates passing through porous medium channel with slip boundary condition. A single fourth order nonlinear ordinary differential equation is obtained using similarity transformation. The resulting boundary value problem is solved using Homotopy Perturbat...

To integrate large systems of locally coupled ordinary differential equations (ODEs) with disparate timescales, we present a multirate method with error control that is based on the Cash-Karp Runge-Kutta (RK) formula. The order of multirate methods often depends on interpolating certain solution components with a polynomial of sufficiently high degree. By using cubic interpolants and analyzing ...