Implicit K-step Adams-type second - derivative block hybrid methods for the solution of stiff initial value problems in ordinary differential equations

Author(s)

Donald, J. Z.; Department of Mathematics, Adamawa State University, Mubi, Nigeria

Abstract

In this paper, we developed a new continuous K-step Adams-Type second-derivative block hybrid methods, using the approach of collocation of the differential system and interpolation of the Taylors series approximate solution at some selected points to get a continuous linear multistep method, which was evaluated at two off-grid points to generate the continuous hybrid linear multistep methods which were evaluated at non-interpolated step points to give CBM’s. The K-step methods were augmented by introducing two off-step points to circumvent the Dahlquist zero barrier and upgrade the order of consistency of the methods. Hence, the basic properties of the methods were investigated and found to be consistent, zero-stable, and convergent. The new methods were tested on stiff and highly stiff equations, the results were found to compete favorably with the existing methods in terms of accuracy and error bound.

Keywords

K-step Adams-Type; second-derivative block hybrid methods; collocation; interpolation; and stiff and highly stiff equations; non-interpolated

Cite this paper

Donald, J. Z. (2022), Implicit K-step Adams-type second – derivative block hybrid methods for the solution of stiff initial value problems in ordinary differential equations, IRESPUB Journal of  Engineering & Computer Sciences. Volume 2, Issue 1, Jan-Feb 2022, Page 10-24

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