Solving SPDEs by a Least Squares Method
نویسنده
چکیده
We present in this paper a useful strategy to solve stochastic partial differential equations (SPDEs) involving stochastic coefficients. Using the Wick-product of higher order and the Wiener-Itô chaos expansion, the SPDEs is reformulated as a large system of deterministic partial differential equations. To reduce the computational complexity of this system, we shall use a decomposition-coordination method. To obtain the chaos coefficients in the corresponding deterministic equations, we use a least square formulation. Once this approximation is performed, the statistics of the numerical solution can be easily evaluated. Keywords—Least squares, Wick product, SPDEs, finite element, Wiener chaos expansion, gradient method.
منابع مشابه
Numerical solution of the spread of infectious diseases mathematical model based on shifted Bernstein polynomials
The Volterra delay integral equations have numerous applications in various branches of science, including biology, ecology, physics and modeling of engineering and natural sciences. In many cases, it is difficult to obtain analytical solutions of these equations. So, numerical methods as an efficient approximation method for solving Volterra delay integral equations are of interest to many res...
متن کاملA meshless discrete Galerkin method for solving the universe evolution differential equations based on the moving least squares approximation
In terms of observational data, there are some problems in the standard Big Bang cosmological model. Inflation era, early accelerated phase of the evolution of the universe, can successfully solve these problems. The inflation epoch can be explained by scalar inflaton field. The evolution of this field is presented by a non-linear differential equation. This equation is considered in FLRW model...
متن کاملTheory of block-pulse functions in numerical solution of Fredholm integral equations of the second kind
Recently, the block-pulse functions (BPFs) are used in solving electromagnetic scattering problem, which are modeled as linear Fredholm integral equations (FIEs) of the second kind. But the theoretical aspect of this method has not fully investigated yet. In this article, in addition to presenting a new approach for solving FIE of the second kind, the theory of both methods is investigated as a...
متن کاملGlobal least squares solution of matrix equation $sum_{j=1}^s A_jX_jB_j = E$
In this paper, an iterative method is proposed for solving matrix equation $sum_{j=1}^s A_jX_jB_j = E$. This method is based on the global least squares (GL-LSQR) method for solving the linear system of equations with the multiple right hand sides. For applying the GL-LSQR algorithm to solve the above matrix equation, a new linear operator, its adjoint and a new inner product are dened. It is p...
متن کاملA Boundary Meshless Method for Neumann Problem
Boundary integral equations (BIE) are reformulations of boundary value problems for partial differential equations. There is a plethora of research on numerical methods for all types of these equations such as solving by discretization which includes numerical integration. In this paper, the Neumann problem is reformulated to a BIE, and then moving least squares as a meshless method is describe...
متن کامل