Borel control and efficient numerical techniques to solve the Allen-Cahn equation governed by temporal multiplicative noise

• Published in: International journal of computer mathematics Vol. 101; no. 9-10; pp. 1152 - 1167
• Main Authors: Ahmed, Nauman, Macías-Díaz, Jorge E., Yasin, Muhammad W., Iqbal, Muhammad S.
• Format: Journal Article
• Language: English
• Published: Abingdon Taylor & Francis 02.10.2024; Taylor & Francis Ltd
• Subjects: Noise control; Nonlinear differential equations; numerical simulations; Partial differential equations; proposed schemes; stability and consistency analyses; Stochastic Allen-Cahn equation; Stochastic models; unique existence

In this manuscript, we investigate a stochastic version of the Allen-Cahn equation, which is a nonlinear partial differential equation from mathematical physics. The stochastic model considers temporal multiplicative noise in the form of the derivative of the standard Wiener process. The existence a...