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A New Methodology for the Development of Efficient Multistep Methods for First-Order Initial Value Problems with Oscillating Solutions V: The Case of the Open Newton–Cotes Differential Formulae

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  • Theodore E. Simos

    (School of Mechanical Engineering, Hangzhou Dianzi University, Er Hao Da Jie 1158, Xiasha, Hangzhou 310018, China
    Center for Applied Mathematics and Bioinformatics, Gulf University for Science and Technology, West Mishref, Mubarak Al-Abdullah 32093, Kuwait
    Section of Mathematics, Department of Civil Engineering, Democritus University of Thrace, 67100 Xanthi, Greece)

Abstract

The author has just published a theory on first-order differential equations that accounts for the phase-lag and amplification-factor calculations using explicit, implicit, and backward differentiation multistep methods. Eliminating the phase-lag and amplification-factor derivatives, his presentation delves into how the techniques’ effectiveness changes. The theory for determining the phase lag and amplification factor, initially established for explicit multistep techniques, will be extended to the Open Newton–Cotes Differential Formulae in this work. The effect of the derivatives of these variables on the efficiency of these calculations will be studied. The novel discovered approach’s symplectic form will be considered next. The discussion of numerical experiment findings and some conclusions on the existing methodologies will conclude in this section.

Suggested Citation

  • Theodore E. Simos, 2024. "A New Methodology for the Development of Efficient Multistep Methods for First-Order Initial Value Problems with Oscillating Solutions V: The Case of the Open Newton–Cotes Differential Formulae," Mathematics, MDPI, vol. 12(23), pages 1-55, November.
  • Handle: RePEc:gam:jmathe:v:12:y:2024:i:23:p:3652-:d:1526555
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    References listed on IDEAS

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    1. Theodore E. Simos, 2024. "A New Methodology for the Development of Efficient Multistep Methods for First-Order IVPs with Oscillating Solutions," Mathematics, MDPI, vol. 12(4), pages 1-32, February.
    2. Chunfeng Wang & Zhongcheng Wang, 2007. "A P-Stable Eighteenth-Order Six-Step Method For Periodic Initial Value Problems," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 18(03), pages 419-431.
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    1. Theodore E. Simos, 2024. "A New Methodology for the Development of Efficient Multistep Methods for First-Order IVPs with Oscillating Solutions," Mathematics, MDPI, vol. 12(4), pages 1-32, February.

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