Abstract
In this paper, we develop a four-step block method for solution of first order initial value problems of ordinary differential equations. The collocation and interpolation approach is adopted to obtain a continuous scheme for the derived method via Shifted Chebyshev Polynomials, truncated after sufficient terms. The properties of the proposed scheme such as order, zero-stability, consistency and convergence are also investigated. The derived scheme is implemented to obtain numerical solutions of some test problems, the result shows that the new scheme competes favorably with exact solution and some existing methods.
Highlights
It is a general knowledge that differential equations model quite a lot of physical problems that occur in many fields of Sciences, Mathematics and Engineering; common among such differential equations are ordinary differential equations
We examine the performance of 4-step block method (4SBM) in terms of accuracy and stability when compared with exact solution (ES)
Each of problems 1 to 4 is solved with the derived 4SBM in their respective intervals with and the results presented alongside exact solutions and absolute errors in 4SBM in the succeeding tables
Summary
It is a general knowledge that differential equations model quite a lot of physical problems that occur in many fields of Sciences, Mathematics and Engineering; common among such differential equations are ordinary differential equations. L. O.: An Efficient 4-Step Block Method for Solution ff First Order Initial Value Problems via Shifted Chebyshev Polynomial minimax polynomials exist and are unique when a function is continuous, they are not easy to compute in general. We shall develop a class of a four step linear multistep method using the Shifted Chebyshev polynomial as basis function and collocation and interpolation approach for the derivation of the method. Method derivation Consider the general form of a first order initial value problem:. The discrete schemes presented in (14) gives the proposed 4-step block method (4SBM) which directly integrates general first order initial value problems of ordinary differential equation. As stated in Henrici (1962), a linear multistep method is zero-stable for any well behaved initial value problem if all roots of the first characteristic polynomial, ( ) lies within the unit circle,. The derived method was shown to be consistent and zero-stable, it is convergent
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