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An Efficient Approach to Numerical Study of the MRLW Equation with B‐Spline Collocation Method

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  • Seydi Battal Gazi Karakoç
  • Turgut Ak
  • Halil Zeybek

Abstract

A septic B‐spline collocation method is implemented to find the numerical solution of the modified regularized long wave (MRLW) equation. Three test problems including the single soliton and interaction of two and three solitons are studied to validate the proposed method by calculating the error norms L2 and L∞ and the invariants I1, I2, and I3. Also, we have studied the Maxwellian initial condition pulse. The numerical results obtained by the method show that the present method is accurate and efficient. Results are compared with some earlier results given in the literature. A linear stability analysis of the method is also investigated.

Suggested Citation

  • Seydi Battal Gazi Karakoç & Turgut Ak & Halil Zeybek, 2014. "An Efficient Approach to Numerical Study of the MRLW Equation with B‐Spline Collocation Method," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:596406
    DOI: 10.1155/2014/596406
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    References listed on IDEAS

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    1. Raslan, K.R., 2009. "Numerical study of the Modified Regularized Long Wave (MRLW) equation," Chaos, Solitons & Fractals, Elsevier, vol. 42(3), pages 1845-1853.
    2. Ramos, J.I., 2007. "Solitary wave interactions of the GRLW equation," Chaos, Solitons & Fractals, Elsevier, vol. 33(2), pages 479-491.
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