The time-step in integration process has two restrictions. The first one is the time step restriction due to accuracy requirement τac and the second one is the time-step restriction due to stability requirement τst. The most of explicit methods have small stability regions and consequently small τst. It obliges us to solve stiff problems with small step size τst << τac. The implicit methods wor...

Stiff behavior occurs in a variety of ODE systems relevant in applications. The notion of stiffness is a phenomenological one, and a stability and error analysis of numerical methods has been based either on simple models or particular problem structures. In particular, stiff initial value problems in standard singular perturbation form are well understood. However, problems of this type exhibi...

In this paper we develop an efficient method based on the Spectral Collocation Method (SCM) and the Variational Iteration Method (VIM) that can be used for the efficient numerical solution of nonlinear stiff/nonstiff two-point Boundary Value Problems (BVPs). The method derived here has the advantage that it does not require the solution of nonlinear systems of equations. We derive the method wh...

We show that there exist classes of explicit numerical integration methods that can handle very stiff problems if the eigenvalues are separated into two clusters, one containing the “stiff,” or fast, components, and one containing the slow components. These methods have large average step sizes relative to the fast components. Conventional implicit methods involve the solution of nonlinear equa...

Integration of a larger stiff system initial value problems emerging from chemical kinetics models requires method that is both efficient and accurate, with large absolute stability region. To determine the solutions ordinary differential equations help in explaining chemically reactive flows, numerical integration methodology known as 3-point variable step block hybrid has been devised. An app...

Stiff-knee gait is a prevalent, debilitating consequence of cerebral palsy in which swingphase knee flexion is substantially diminished. Approximately 3 out of every 1,000 children manifest one or more of the symptoms of cerebral palsy (CDC, 2004). Stiff knee gait results in a number of related gait problems including tripping and foot-dragging due to inadequate toe clearance (Sutherland and Da...