Solution of the 1D KPZ Equation by Explicit Methods
Okhunjon SayfidinovInstitute of Machine and Product Design, University of Miskolc, 3515 Miskolc, HungaryGabriella BognárInstitute of Machine and Product Design, University of Miskolc, 3515 Miskolc, HungaryEndre KovácsInstitute of Physics and Electrical Engineering, University of Miskolc, 3515 Miskolc, Hungary
2022en
ABI
Annotatsiya
The Kardar–Parisi-Zhang (KPZ) equation is examined using the recently published leapfrog–hopscotch (LH) method as well as the most standard forward time centered space (FTCS) scheme and the Heun method. The methods are verified by reproducing an analytical solution. The performance of each method is then compared by calculating the average and the maximum differences among the results and displaying the runtimes. Numerical tests show that due to the special symmetry in the time–space discretisation, the new LH method clearly outperforms the other two methods. In addition, we discuss the effect of different parameters on the solutions.
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