Abstract
In this paper, we developed a new continuous block method by the method of interpolation and collocation to derive new scheme. We adopted the use of power series as a basis function for approximate solution. We evaluated at off grid points to get a continuous hybrid multistep method. The continuous hybrid 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, zero stable and convergent. The results were found to compete favorably with the existing methods in terms of accuracy and error bound. In particular, the scheme was found to have a large region of absolute stability. The new method was tested on real life problem namely: Dynamic model.
Highlights
We considered the method of approximate solution of the general second order initial value problem of the form
We propose a new one-twelfth step continuous hybrid block method for the numerical integration of second order initial value problems with constant step-size which is implemented in block mode
According to [3], the first condition is a sufficient condition for the associated block method to be consistent
Summary
We considered the method of approximate solution of the general second order initial value problem of the form. (2015) A New One-Twelfth Step Continuous Block Method for the Solution of Modeled Problems of Ordinary Differential Equations. This block method has the properties of Runge-kutta method for being self-starting and does not require development of separate predictors or starting values. We propose a new one-twelfth step continuous hybrid block method for the numerical integration of second order initial value problems with constant step-size which is implemented in block mode. The paper is organized as followed: Section 2 considers the mathematical formulation of the method.
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