A Proposed Stochastic Finite Difference Approach Based on Homogenous Chaos Expansion
| Autor: | Osama H. Galal |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2013 |
| Předmět: |
Continuous-time stochastic process
Partial differential equation Article Subject Applied Mathematics lcsh:Mathematics Mathematical analysis Stochastic calculus Finite difference lcsh:QA1-939 Stochastic partial differential equation Stochastic differential equation Quantum stochastic calculus Stochastic optimization Mathematics |
| Zdroj: | Journal of Applied Mathematics, Vol 2013 (2013) J. Appl. Math. |
| ISSN: | 1687-0042 |
| Popis: | This paper proposes a stochastic finite difference approach, based on homogenous chaos expansion (SFDHC). The said approach can handle time dependent nonlinear as well as linear systems with deterministic or stochastic initial and boundary conditions. In this approach, included stochastic parameters are modeled as second-order stochastic processes and are expanded using Karhunen-Loève expansion, while the response function is approximated using homogenous chaos expansion. Galerkin projection is used in converting the original stochastic partial differential equation (PDE) into a set of coupled deterministic partial differential equations and then solved using finite difference method. Two well-known equations were used for efficiency validation of the method proposed. First one being the linear diffusion equation with stochastic parameter and the second is the nonlinear Burger's equation with stochastic parameter and stochastic initial and boundary conditions. In both of these examples, the probability distribution function of the response manifested close conformity to the results obtained from Monte Carlo simulation with optimized computational cost. |
| Databáze: | OpenAIRE |
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