Energy SSP-IMEX Runge–Kutta methods for the Cahn–Hilliard equation

• Huailing Song ^[1]
  1. [1] Hunan University

     Hunan University

     China

     
• Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 292, Nº 1 (15 January 2016), 2016, págs. 576-590
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen

  • We consider the Cahn–Hilliard equation, which describes phase separation phenomenon. The equation is discretized by using a fourth-order compact difference scheme in space and strong-stability-preserving (SSP) implicit–explicit (IMEX) Runge–Kutta methods in time. The new methods have two distinct features: (1) the large time steps can be used in the numerical simulation because the energy is stable, and (2) the energy functional decreases by time. Unconditional energy-stability of first-order and second-order methods are proved. Numerical experiments are given to demonstrate the performance of the proposed methods.