An exponentially-fitted method for singularly perturbed, one-dimensional, linear, convection-diffusion-reaction equations in equally-spaced grids is presented. The method is based on the implicit discretization of the time derivative, freezing of the ...
In this paper, we apply positivity-preserving local discontinuous Galerkin (LDG) methods to solve parabolic equations with blow-up solutions. This model is commonly used in combustion problems. However, previous numerical methods are mainly based on a ...
We build a simple and general class of finite difference schemes for first order Hamilton-Jacobi (HJ) Partial Differential Equations. These filtered schemes are convergent to the unique viscosity solution of the equation. The schemes are accurate: we ...
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