
Stability and error analysis of a class of highorder IMEX schemes for Navierstokes equations with periodic boundary conditions
We construct highorder semidiscreteintime and fully discrete (with F...
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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 ...
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Unconditionally energy stable and firstorder accurate numerical schemes for the heat equation with uncertain temperaturedependent conductivity
In this paper, we present firstorder accurate numerical methods for sol...
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A Relaxation/Finite Difference discretization of a 2D Semilinear Heat Equation over a rectangular domain
We consider an initial and Dirichlet boundary value problem for a semili...
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Analysis of boundary effects on PDEbased sampling of WhittleMatérn random fields
We consider the generation of samples of a meanzero Gaussian random fie...
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Effects of roundtonearest and stochastic rounding in the numerical solution of the heat equation in low precision
Motivated by the advent of machine learning, the last few years saw the ...
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Algorithm for numerical solutions to the kinetic equation of a spatial population dynamics model with coalescence and repulsive jumps
An algorithm is proposed for finding numerical solutions of a kinetic eq...
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Error Inhibiting Schemes for Initial Boundary Value Heat Equation
In this paper, we elaborate the analysis of some of the schemes which were presented in arXiv:1711.07926 for the heat equation with periodic boundary conditions. We adopt this methodology to derive finitedifference schemes for heat equation with Dirichlet and Neumann boundary conditions, whose convergence rates are higher than their truncation errors. We call these schemes error inhibiting schemes. When constructing a semidiscrete approximation to a partial differential equation (PDE), a discretization of the spatial operator has to be derived. For stability, this discrete operator must be semibounded. Under this semiboundness, the LaxRichtmyer equivalence theorem assures that the scheme converges at most, as the order of the error will be at most of the order of the truncation error. Usually, the error is in indeed of the order of the truncation error. In this paper, we demonstrate that schemes can be constructed such that their errors are smaller than their truncation errors. This property can enable us design schemes which are more efficient than standard schemes.
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