A new approach for the numerical approximation of modified Korteweg–de Vries equation

Fayyaz Ahmad, Shafiq Ur Rehman and Aiman Zara

Mathematics and Computers in Simulation (MATCOM), 2023, vol. 203, issue C, 189-206

Abstract: We present and illustrate a new numerical scheme for the numerical approximation of modified Korteweg–de Vries (mKdV) equation. The spatial derivatives involved in the modified Korteweg–de Vries equation are approximated by smoothing Kernel technique. Whereas, for the time integration, we use Crank–Nicolson integrator. The constant of mass conservation (I1), constant of energy conservation (I2), and the constant of momentum conservation (I3) provide much insight about the conservative nature of the proposed numerical scheme. The numerical testing is performed on a collection of three test problems.

Keywords: Modified Korteweg–de Vries equation (mKdV); Solitary waves; Smoothing Kernel method (search for similar items in EconPapers)
Date: 2023
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:203:y:2023:i:c:p:189-206

DOI: 10.1016/j.matcom.2022.06.021

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