Hybrid block formulae whose eigenvalues of Jacobian matrices are close to the imaginary axis of the complex plane

Authors

  • J. E. Kona Department of Mathematics and Statistics, University of Delta, Agbor, Delta State
  • K. O. Muka Department of Mathematics, University of Benin, Benin City, Edo State

Keywords:

A-stable, Stiff initial value problem, Complex plain, Hybrid block method

Abstract

Methods for integrating stiff initial value problems are required to be A-stable. Of great interest are A-stable methods whose Jacobian matrices have their eigenvalues close to the imaginary axis of the complex plane. This class of A-stable methods are very rare. This paper is on the development of a new family of A-stable hybrid block method whose Jacobian matrices possess eigenvalues on the imaginary of the complex plane via interpolation and collocation techniques. The family of methods developed herein are A-stable for order p ≤ 18. Numerical solutions generated by the new method are compared with existing methods in the literature. The numerical results show that the new class of methods are more efficient and accurate.

Dimensions

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Published

2024-09-02

How to Cite

Hybrid block formulae whose eigenvalues of Jacobian matrices are close to the imaginary axis of the complex plane. (2024). Recent Advances in Natural Sciences, 2(2), 74. https://doi.org/10.61298/rans.2024.2.2.74

Issue

Volume 2, Issue 2, December 2024 (In Progress)

Section

Articles
Copyright & Licensing

Copyright (c) 2024 J. E. Kona, K. O. Muka

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

Hybrid block formulae whose eigenvalues of Jacobian matrices are close to the imaginary axis of the complex plane. (2024). Recent Advances in Natural Sciences, 2(2), 74. https://doi.org/10.61298/rans.2024.2.2.74