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A family of matrix coefficient formulas for solving ordinary differential equations

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  • Chang, Shuenn-Yih

Abstract

A matrix form of coefficients is applied to develop a new family of one-step explicit methods. Clearly, this type of methods is different from the conventional methods that have scalar constant coefficients. This novel family of methods is governed by a free parameter and is characterized by problem dependency, where the initial physical properties to define the problem under analysis are applied to form the coefficients of the difference formula. In general, it can simultaneously combine A-stability, second order accuracy and explicit implementation. As a result, it is best suited to solve systems of nonlinear first order stiff ordinary differential equations since it is of high computational efficiency in contrast to conventional implicit methods.

Suggested Citation

  • Chang, Shuenn-Yih, 2022. "A family of matrix coefficient formulas for solving ordinary differential equations," Applied Mathematics and Computation, Elsevier, vol. 418(C).
    • Handle: RePEc:eee:apmaco:v:418:y:2022:i:c:s0096300321008948
    DOI: 10.1016/j.amc.2021.126811
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    References listed on IDEAS

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    1. Mehmet Tarik Atay & Okan Kilic, 2013. "The Semianalytical Solutions for Stiff Systems of Ordinary Differential Equations by Using Variational Iteration Method and Modified Variational Iteration Method with Comparison to Exact Solutions," Mathematical Problems in Engineering, Hindawi, vol. 2013, pages 1-11, April.
    2. D’Ambrosio, Raffaele & Jackiewicz, Zdzislaw, 2011. "Construction and implementation of highly stable two-step continuous methods for stiff differential systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(9), pages 1707-1728.
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    Cited by:

    1. Soradi-Zeid, Samaneh & Mesrizadeh, Mehdi, 2023. "On the convergence of finite integration method for system of ordinary differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 167(C).

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