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

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

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.

Suggested Citation

  • Ahmadinia, M. & Abbasi, M. & Emrani, A.R., 2024. "A novel A-stable method of order of accuracy three, based on optimization for solving initial value problems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 226(C), pages 184-203.
    • Handle: RePEc:eee:matcom:v:226:y:2024:i:c:p:184-203
    DOI: 10.1016/j.matcom.2024.06.020
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    References listed on IDEAS

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    1. Ramos, Higinio & Singh, Gurjinder, 2017. "A tenth order A-stable two-step hybrid block method for solving initial value problems of ODEs," Applied Mathematics and Computation, Elsevier, vol. 310(C), pages 75-88.
    2. Singh, Gurjinder & Garg, Arvind & Kanwar, V. & Ramos, Higinio, 2019. "An efficient optimized adaptive step-size hybrid block method for integrating differential systems," Applied Mathematics and Computation, Elsevier, vol. 362(C), pages 1-1.
    3. Ramos, Higinio & Singh, Gurjinder & Kanwar, V. & Bhatia, Saurabh, 2015. "Solving first-order initial-value problems by using an explicit non-standard A-stable one-step method in variable step-size formulation," Applied Mathematics and Computation, Elsevier, vol. 268(C), pages 796-805.
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