Opuscula Math. 34, no. 2 (2014), 443-456
Method of lines for parabolic stochastic functional partial differential equations
Abstract. We approximate parabolic stochastic functional differential equations substituting the derivatives in the space variable by finite differences. We prove the stability of the method of lines corresponding to a parabolic SPDE driven by Brownian motion.
Keywords: stochastic partial differential equations, stability of the method of lines, white noise, Volterra stochastic equations.
Mathematics Subject Classification: 35R60, 49M25.