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http://dx.doi.org/10.12941/jksiam.2021.25.224

IMPLICIT-EXPLICIT SECOND DERIVATIVE LMM FOR STIFF ORDINARY DIFFERENTIAL EQUATIONS  

OGUNFEYITIMI, S.E. (ADVANCED RESEARCH LABORATORY, DEPARTMENT OF MATHEMATICS, UNIVERSITY OF BENIN)
IKHILE, M.N.O. (ADVANCED RESEARCH LABORATORY, DEPARTMENT OF MATHEMATICS, UNIVERSITY OF BENIN)
Publication Information
Journal of the Korean Society for Industrial and Applied Mathematics / v.25, no.4, 2021 , pp. 224-261 More about this Journal
Abstract
The interest in implicit-explicit (IMEX) integration methods has emerged as an alternative for dealing in a computationally cost-effective way with stiff ordinary differential equations arising from practical modeling problems. In this paper, we introduce implicit-explicit second derivative linear multi-step methods (IMEX SDLMM) with error control. The proposed IMEX SDLMM is based on second derivative backward differentiation formulas (SDBDF) and recursive SDBDF. The IMEX second derivative schemes are constructed with order p ranging from p = 1 to 8. The methods are numerically validated on well-known stiff equations.
Keywords
implicit-explicit (IMEX) Schemes; Second derivative linear multistep methods (SDLMM); recursive SDLMM; second derivative backward differentiation formulas (SDBDFs); difference corrected SDBDFs; stiff equation;
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