Hybrid block formulae whose eigenvalues of Jacobian matrices are close to the imaginary axis of the complex plane
Year: 2024
Type: article
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.
Authors: James Kona, Kingsley Muka
Institutions: University of Delta Agbor, University of Benin
Language: English
Subfield: Numerical Analysis
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4402126694