Perspective chapter: Numerical solutions for modelling complex systems with Stochastic Differential and Partial Differential Equations (SDEs/SPDEs)

Abstract

Understanding phenomena ranging from biological processes to financial markets involves uncertainty. Stochastic Differential Equations (SDEs) and Stochastic Partial Differential Equations (SPDEs) serve as robust mathematical frameworks for modelling such systems. Given the stochastic influences within these models, comprehending the dynamics of complex systems becomes pivotal for accurately predicting system behaviour. However, traditional numerical techniques frequently encounter challenges in effectively addressing the intricacies and stochastic properties inherent in these equations. This chapter explores several numerical methods that offer streamlined and dependable solutions capable of handling the complexities inherent in stochastic differential and partial differential equations. Also, numerical challenges associated with these methods are discussed and the solution strategies are also suggested.