Solution of the 1D KPZ Equation by Explicit Methods

被引：4
作者：
Sayfidinov, Okhunjon [1 ]
Bognar, Gabriella [1 ]
Kovacs, Endre [2 ]
机构：
[1] Univ Miskolc, Inst Machine & Prod Design, H-3515 Miskolc, Hungary
[2] Univ Miskolc, Inst Phys & Elect Engn, H-3515 Miskolc, Hungary
来源：
SYMMETRY-BASEL | 2022年 / 14卷 / 04期
关键词：
KPZ equation; nonlinear PDEs; explicit time integration; stable numerical methods; leapfrog-hopscotch method; FTCS scheme; PARISI-ZHANG EQUATION; SURFACE GROWTH; NUMERICAL-SOLUTION; INSTABILITY; BEHAVIOR; MODELS;
D O I：
10.3390/sym14040699
中图分类号：
O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];
学科分类号：
07 ; 0710 ; 09 ;
摘要：
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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页数：14
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