# High Order Multi-block Boundary-value Integration Methods for Stiff ODEs

• S. E. Ogunfeyitimi Department of Mathematics, University of Benin, Benin City, Nigeria
• M. N. O. Ikhile Department of Mathematics, University of Benin, Benin City, Nigeria
Keywords: second derivative multi-block boundary value methods, Enright's methods, Wiener-Hopf factorization, stiff systems

### Abstract

In this paper, we present a new family of multi-block boundary value integration methods based on the Enright second derivative type-methods for differential equations. We rigorously show that this class of multi-block methods are generally \$A_{k_1,k_2}\$-stable for all block number by verifying through employing the Wiener-Hopf factorization of a matrix polynomial to determine the root distribution of the stability polynomial. Further more, the correct implementation procedure is as well determine by Wiener-Hopf factorization. Some numerical results are presented and a comparison is made with some existing methods. The new methods which output multi-block of solutions of the ordinary differential equations on application, and are unlike the conventional linear multistep methods which output a solution at a point or the conventional boundary value methods and multi-block methods which output a block of solutions per step. The second derivative multi-block boundary value integration methods are a new approach at obtaining very large scale integration methods for the numerical solution of differential equations.

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Published
2022-06-16
How to Cite
Ogunfeyitimi, S. E., & Ikhile, M. N. O. (2022). High Order Multi-block Boundary-value Integration Methods for Stiff ODEs. Earthline Journal of Mathematical Sciences, 10(1), 125-168. https://doi.org/10.34198/ejms.10122.125168
Section
Articles