An approximate solution for stochastic Burgers’ equation driven by white noise. (English) Zbl 1513.65011
Summary: This paper proposes an approximate solution based on two-dimensional shifted Legendre polynomials, together with its operational matrices of integration and stochastic integration for solving stochastic Burgers’ equations with a space-uniform white noise and with variable coefficients. The aforementioned operational matrices transform the problem under consideration into a system of algebraic equations. The error analysis in the \(L^2\) norm for the proposed method is discussed in detail. The transformation is done by taking into account the initial and boundary conditions. Hence, the proposed method is very simple for solving such problems. Numerical examples discussed confirm the efficiency and accuracy of the proposed method. A simulation study was carried out. An algorithm was developed and implemented on Maple software.
MSC:
| 65C30 | Numerical solutions to stochastic differential and integral equations |
| 60H35 | Computational methods for stochastic equations (aspects of stochastic analysis) |
| 60H15 | Stochastic partial differential equations (aspects of stochastic analysis) |
| 60H40 | White noise theory |
| 35Q53 | KdV equations (Korteweg-de Vries equations) |
| 35R60 | PDEs with randomness, stochastic partial differential equations |
Keywords:
stochastic partial differential equations; Burgers’ equations; shifted Legendre polynomials; operational matrices; error analysisSoftware:
MapleReferences:
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