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Higher order Haar wavelet method integrated with strang splitting for solving regularized long wave equation

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  • Bulut, Fatih
  • Oruç, Ömer
  • Esen, Alaattin

Abstract

In this paper, we are going to utilize newly developed Higher Order Haar wavelet method (HOHWM) and classical Haar wavelet method (HWM) to numerically solve the Regularized Long Wave (RLW) equation. Spatial variable of the RLW equation is treated with HOHWM and HWM separately. On the other hand temporal variable is discretized by finite differences combined with Strang splitting approach. The presented methods applied to three different test problems and the obtained results are given in tables as well as depicted in figures. The obtained results are compared with analytical results wherever they exist. The error norms L2 and L∞ and invariants I1, I2 and I3 are used to show the accuracy of the methods when comparing the present results with those in the literature.

Suggested Citation

  • Bulut, Fatih & Oruç, Ömer & Esen, Alaattin, 2022. "Higher order Haar wavelet method integrated with strang splitting for solving regularized long wave equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 197(C), pages 277-290.
    • Handle: RePEc:eee:matcom:v:197:y:2022:i:c:p:277-290
    DOI: 10.1016/j.matcom.2022.02.006
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    References listed on IDEAS

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    1. Lepik, Ü., 2005. "Numerical solution of differential equations using Haar wavelets," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 68(2), pages 127-143.
    2. S. Kutluay & A. Esen, 2006. "A finite difference solution of the regularized long-wave equation," Mathematical Problems in Engineering, Hindawi, vol. 2006, pages 1-14, March.
    3. Ömer Oruç & Alaattin Esen & Fatih Bulut, 2016. "A Haar wavelet collocation method for coupled nonlinear Schrödinger–KdV equations," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 27(09), pages 1-16, September.
    4. Mart Ratas & Jüri Majak & Andrus Salupere, 2021. "Solving Nonlinear Boundary Value Problems Using the Higher Order Haar Wavelet Method," Mathematics, MDPI, vol. 9(21), pages 1-12, November.
    5. Hsiao, Chun-Hui, 1997. "State analysis of linear time delayed systems via Haar wavelets," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 44(5), pages 457-470.
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