An explicit numerical scheme for the computer simulation of the stochastic transport equation

• Published in: Communications in nonlinear science & numerical simulation Vol. 110; p. 106378
• Main Authors: de la Cruz, H., Olivera, C.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.07.2022; Elsevier Science Ltd
• Subjects: Computational methods; Local linearization approach; Numerical analysis; Numerical integration; Numerical simulation of stochastic systems; Random differential equations; Simulation; Stochastic models; Stochastic transport equation; Transport equations; Computational methods; Numerical simulation of stochastic systems; Local linearization approach; Stochastic transport equation; Random differential equations
• ISSN: 1007-5704; 1878-7274
• DOI: 10.1016/j.cnsns.2022.106378

A computational method for the numerical integration of the stochastic transport equation is proposed. We develop an approach to construct an explicit numerical scheme for the effective simulation of trajectories of solutions of this equation. Results on its convergence and details on its efficient computational implementation are presented. The performance of the proposed scheme is illustrated by means of computer simulations. •An easy-to-implement explicit method is proposed for stochastic transport equations.•The proposed approach is completely different from others available in the literature.•The computational burden is basically the same as solving systems of linear equations.•The approach can be used for transport equations driven by low regularity processes.