Upwind Finite-Volume Solution of Stochastic Burgers’ Equation

The Upwind Finite Volume Element Method for Two-Dimensional Burgers Equation

and Applied Analysis 3 where P l (V) (l = 0, 1) denotes the set of polynomials on V with a degree of not more than l. Multiplying (6a) by test function z ∈ V h and integrating by parts yield ( ∂θ ∂t , z) + B 1 (θ; θ, z) + B 2 (θ; θ, z) + A (θ, z) = 0, ∀z ∈ V h , (9)

Multidimensional Stochastic Burgers Equation

We consider multidimensional stochastic Burgers equation on the torus T and the whole space R . In both cases we show that for positive viscosity ν > 0 there exists a unique strong global solution in L for p > d. In the case of torus we also establish a uniform in ν a priori estimate and consider a limit ν ↘ 0 for potential solutions. In the case of R uniform with respect to ν a priori estimate...

Numerical Solution of Heun Equation Via Linear Stochastic Differential Equation

In this paper, we intend to solve special kind of ordinary differential equations which is called Heun equations, by converting to a corresponding stochastic differential equation(S.D.E.). So, we construct a stochastic linear equation system from this equation which its solution is based on computing fundamental matrix of this system and then, this S.D.E. is solved by numerically methods. Moreo...

On Numerical Approximation of Stochastic Burgers’ Equation

Random Periodic Solutions of Stochastic Burgers Equation

The dynamics of randomly forced Burgers and Euler-Lagrange equations in S 1 × R d−1 in the case when there is only one one-sided minimizer in a compact subset of S 1 × R d−1 is studied. The existence of random invariant periodic minimizer orbits and periodicity of the stationary solution of the stochastic Burgers equations are obtained.