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A modified Gautschi’s method without order reduction when integrating boundary value nonlinear wave problems

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  • Cano, B.
  • Moreta, M.J.

Abstract

In this paper we analyse the order reduction which turns up when integrating nonlinear wave problems with non-homogeneous and time-dependent boundary conditions with the well-known Gautschi’s method. Moreover, a technique is suggested to avoid that order reduction so that the classical local order 4 and global order 2 are recovered. On the other hand, the usual approximation for the derivative which is used together with this method is also analysed and a substantial improvement is suggested. Some numerical results are shown which corroborate the performed analysis.

Suggested Citation

  • Cano, B. & Moreta, M.J., 2020. "A modified Gautschi’s method without order reduction when integrating boundary value nonlinear wave problems," Applied Mathematics and Computation, Elsevier, vol. 373(C).
    • Handle: RePEc:eee:apmaco:v:373:y:2020:i:c:s0096300319310148
    DOI: 10.1016/j.amc.2019.125022
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    References listed on IDEAS

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    1. Einkemmer, Lukas & Moccaldi, Martina & Ostermann, Alexander, 2018. "Efficient boundary corrected Strang splitting," Applied Mathematics and Computation, Elsevier, vol. 332(C), pages 76-89.
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    Cited by:

    1. Isaías Alonso-Mallo & Ana M. Portillo, 2021. "Integrating Semilinear Wave Problems with Time-Dependent Boundary Values Using Arbitrarily High-Order Splitting Methods," Mathematics, MDPI, vol. 9(10), pages 1-24, May.

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