Half-Step Continuous Block Method for the Solutions of Modeled Problems of Ordinary Differential Equations

Abstract

In this paper, we developed a new continuous block method using the approach of collocation of the differential system and interpolation of the power series approximate solution. A constant step length within a half step interval of integration was adopted. We evaluated at grid and off grid points to get a continuous linear multistep method. The continuous linear multistep method is solved for the independent solution to yield a continuous block method which is evaluated at selected points to yield a discrete block method. The basic properties of the block method were investigated and found to be consistent and zero stable hence convergent. The new method was tested on real life problems namely: SIR model, Growth model and Mixture Model. The results were found to compete favorably with the existing methods in terms of accuracy and error bound.

Numerical Strategies for the System of First Order IVPs Using Block Hybrid Extended Trapezoidal Multistep Method of Second Kind for Stiff ODEs

“…The name of this class of models derives from the fact that they involves coupled equations relating the number of susceptible people ( ) S t , number of people infected ( ) I t and the number of people who have recovered ( ) R t . This is a good and simple model for many infectious diseases including measles, mumps and rubella [13][14][15]. The SIR Trapezoidal Multistep Method of Second Kind for Stiff ODEs model is described by the three coupled equations.…”

A New One-Twelfth Step Continuous Block Method for the Solution of Modeled Problems of Ordinary Differential Equations

“…are coefficients to be determined and is a polynomial of degree 1 r s + − . We construct a k-step collocation method (MCM) by imposing the following conditions on(2) …”