
Error Inhibiting Schemes for Initial Boundary Value Heat Equation
In this paper, we elaborate the analysis of some of the schemes which we...
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Large deviations principles for symplectic discretizations of stochastic linear Schrödinger Equation
In this paper, we consider the large deviations principles (LDPs) for th...
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On generating fully discrete samples of the stochastic heat equation on an interval
Generalizing an idea of Davie and Gaines (2001), we present a method for...
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Upstream mobility Finite Volumes for the Richards equation in heterogenous domains
This paper is concerned with the Richards equation in a heterogeneous do...
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Combined use of mixed and hybrid finite elements method with domain decomposition and spectral methods for a study of renormalization for the KPZ model
The focus of this work is the numerical approximation of timedependent ...
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Secondorder accurate BGK schemes for the special relativistic hydrodynamics with the Synge equation of state
This paper extends the secondorder accurate BGK finite volume schemes f...
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Exact Phase Transitions of Model RB with SlowerGrowing Domains
The second moment method has always been an effective tool to lower boun...
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Weak intermittency and second moment bound of a fully discrete scheme for stochastic heat equation
In this paper, we first prove the weak intermittency, and in particular the sharp exponential order Cλ^4t of the second moment of the exact solution of the stochastic heat equation with multiplicative noise and periodic boundary condition, where λ>0 denotes the level of the noise. In order to inherit numerically these intrinsic properties of the original equation, we introduce a fully discrete scheme, whose spatial direction is based on the finite difference method and temporal direction is based on the θscheme. We prove that the second moment of numerical solutions of both spatially semidiscrete and fully discrete schemes grows at least as exp{Cλ^2t} and at most as exp{Cλ^4t} for large t under natural conditions, which implies the weak intermittency of these numerical solutions. Moreover, a renewal approach is applied to show that both of the numerical schemes could preserve the sharp exponential order Cλ^4t of the second moment of the exact solution for large spatial partition number.
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