Tiwari, ParulKulasiri, DonSamarasinghe, SandhyaKulasiri, Don2024-09-232024-06-272024-07-31978-1-83769-550-8https://hdl.handle.net/10182/17622Understanding 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.26 pages, 7 chapters© 2024 The Author(s). Licensee IntechOpen.Brownian motionCameron-Martin basisstochastic differential and partial differential equationsstochastic spectral methodsWiener chaos expansionBook Chapter10.5772/intechopen.1005429978-1-83769-551-5ANZSRC::490510 Stochastic analysis and modellingANZSRC::310114 Systems biologyhttps://creativecommons.org/licenses/by/4.0/Attribution