Article2003

ON SOLVING STOCHASTIC INITIAL-VALUE DIFFERENTIAL EQUATIONS

13 citations0/0 files storedMathematical Models and Methods in Applied Sciences

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Probabilistic and Robust Engineering Design Advanced Numerical Methods in Computational Mathematics Numerical methods for differential equations

Abstract

This paper addresses the issues involved in solving systems of linear ODE's with stochastic coefficients and loadings described by the Karhunen–Loeve expansion. The Karhunen–Loeve expansion is used to discretize random functions into a denumerable set of uncorrelated random variables, thus providing us for transforming this problem into an equivalent deterministic one. Perturbation error estimates and a priori error estimates between the exact solution and the finite element solution in the framework of Sobolev space are given. The method of successive approximations for finite element solutions is analyzed.

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References

1991Stochastic Finite Elements: A Spectral Approach 1998Stochastic Differential Equations 2014Stochastic Integration and Differential Equations : A New Approach 1983Stochastic Finite Element Analysis of Simple Beams 2001Solution of stochastic partial differential equations using Galerkin finite element techniques 1994Numerical solution of stochastic differential equations 1996Numerical solution of spectral stochastic finite element systems 2002On solving elliptic stochastic partial differential equations

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2014A priori error estimation for the stochastic perturbation method 2015Parametric models for samples of random functions

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