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...

This part is concerned with the numerical solution of initial value problems for systems of ordinary differential equations. We will introduce the most basic one-step methods, beginning with the most basic Euler scheme, and working up to the extremely popular Runge–Kutta fourth order method that can be successfully employed in most situations. We end with a brief discussion of stiff differentia...

The method of exact linearization nonlinear ordinary differential equations (ODE) of order n suggested by one of the authors is demonstrated in [1, 2]. This method is based on the factorization of nonlinear ODE through the first order nonlinear differential the operators, and is also based on using both point and nonpoint, local and nonlocal transformations. Exact linearization of autonomous th...