A novel A-stable method of order of accuracy three, based on optimization for solving initial value problems

M. Ahmadinia, M. Abbasi and A.R. Emrani

Mathematics and Computers in Simulation (MATCOM), 2024, vol. 226, issue C, 184-203

Abstract: This paper presents a novel A-stable nonlinear method of order of accuracy three, based on optimization for solving the first-order initial value problems. The A-stability is proven and the consistency of order three is investigated as well. The convergence of the method is established under certain assumptions. Additionally, a second-order method is derived based on this approach, and a variable step size formulation is implemented using the second and third-order methods to enhance efficiency. Numerical examples provided in the paper demonstrate the validity of the theory and underscore the advantages of the method compared to three other A-stable methods of order three, including an implicit RK method, a Rosenbrock method, and an explicit (nonstandard) method.

Keywords: Region of absolute stability; Order of method; A-stability; Consistency; Variable step size; Stiff systems; Numerical integration (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:226:y:2024:i:c:p:184-203

DOI: 10.1016/j.matcom.2024.06.020

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