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Modified Hybrid Method with Four Stages for Second Order Ordinary Differential Equations

Author

Listed:
  • Faieza Samat

    (GENIUS@Pintar National Gifted Centre, Universiti Kebangsaan Malaysia, Selangor 43600, Malaysia)

  • Eddie Shahril Ismail

    (Department of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, Selangor 43600, Malaysia)

Abstract

A modified explicit hybrid method with four stages is presented, with the first stage exactly integrating exp( wx ), while the remaining stages exactly integrate sin( wx ) and cos( wx ). Special attention is paid to the phase properties of the method during the process of parameter selection. Numerical comparisons of the proposed and existing hybrid methods for several second-order problems show that the proposed method gives high accuracy in solving the Duffing equation and Kramarz’s system.

Suggested Citation

  • Faieza Samat & Eddie Shahril Ismail, 2021. "Modified Hybrid Method with Four Stages for Second Order Ordinary Differential Equations," Mathematics, MDPI, vol. 9(9), pages 1-7, May.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:9:p:1028-:d:547690
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    References listed on IDEAS

    as
    1. Li, Jiyong & Deng, Shuo, 2018. "Trigonometrically fitted multi-step RKN methods for second-order oscillatory initial value problems," Applied Mathematics and Computation, Elsevier, vol. 320(C), pages 740-753.
    2. Li, Jiyong, 2018. "Trigonometrically fitted three-derivative Runge–Kutta methods for solving oscillatory initial value problems," Applied Mathematics and Computation, Elsevier, vol. 330(C), pages 103-117.
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