A direct meshless local collocation method for solving stochastic Cahn–Hilliard–Cook and stochastic Swift–Hohenberg equations. (January 2019)

• Record Type: Journal Article
• Authors: Abbaszadeh, Mostafa; Khodadadian, Amirreza; Parvizi, Maryam; Dehghan, Mehdi; Heitzinger, Clemens
• Is Part Of: Engineering analysis with boundary elements. Volume 98(2019)
• Page Start: 253
• Page End: 264
• Publication Date: 2019-01
• Subjects: Meshless methods -- Local weak form -- Stochastic Cahn–Hilliard–Cook equation -- Stochastic Swift–Hohenberg equation -- Euler–Maruyama method -- Direct meshless local Petrov–Galerkin (DMLPG) method; 35R60 -- 60H15 -- 65L60; Boundary element methods -- Periodicals; Engineering mathematics -- Periodicals; Équations intégrales de frontière, Méthodes des -- Périodiques; Mathématiques de l'ingénieur -- Périodiques; Boundary element methods; Engineering mathematics; Periodicals; 620.00151
• DOI: 10.1016/j.enganabound.2018.10.021
• Languages: English
• ISSNs: 0955-7997

Abstract

Abstract: In this study, the direct meshless local Petrov–Galerkin (DMLPG) method has been employed to solve the stochastic Cahn–Hilliard–Cook and Swift–Hohenberg equations. First of all, we discretize the temporal direction by a finite difference scheme. In order to obtain a fully discrete scheme the direct meshless local collocation method is used to discretize the spatial variable and the Euler–Maruyama method is used for time discretization. The used method is a truly meshless technique. In order to illustrate the efficiency and accuracy of the explained numerical technique, we study two stochastic models with their applications in biology and engineering, i.e., the stochastic Cahn–Hilliard–Cook equation and a stochastic Swift–Hohenberg model.