Implicit second-derivative runge-kutta collocation methods for the solution of systems of initial value problems

Author(s)

Donald J. Z^1*, G.M Kumleng², and Yusuf. S² ; ^1,2Department of Mathematics, Adamawa State University, Mubi, Nigeria, ²Department of Mathematics, University of Jos, Plateau State, Nigeria

Abstract

In this paper, we present a class of implicit Second-derivative Runge-Kutta collocation methods designed for the numerical solution of systems of initial value problems that are derived and studied. We also discuss the difficulty associated with large regions of absolute stability. In this case, one must take advantage of the second derivative terms in the methods. We involve the introduction of collocation at the two endpoints of the integration interval in addition to the Gaussian interior collocation points and also the introduction of a different class of basic second derivative methods. With these modifications, fewer function evaluations per step are achieved. The stability and consistency properties of the methods are investigated, with the solution curves of the new methods. Numerical examples are given to illustrate the accuracy and efficiency of the proposed methods.

Keywords

gaussian interior points; block hybrid scheme; continuous scheme; system of equations; second-derivative runge-Kutta methods

Cite this paper

Donald, J. Z., Kumleng, G. M., Yusuf, S. (2021), Implicit second-derivative runge-kutta collocation methods for the solution of systems of initial value problems, IRESPUB Journal of  Engineering & Computer Sciences. Volume 1, Issue 1, Nov-Dec 2021, Page 15-32

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