Implicit---Explicit Runge---Kutta Schemes and Applications to Hyperbolic Systems with Relaxation
Journal of Scientific Computing
Numerical approximation of the viscous quantum hydrodynamic model for semiconductors
Applied Numerical Mathematics
Journal of Computational Physics
On Stability, Monotonicity, and Construction of Difference Schemes I: Theory
SIAM Journal on Scientific Computing
On Stability, Monotonicity, and Construction of Difference Schemes II: Applications
SIAM Journal on Scientific Computing
Applied Numerical Mathematics
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Many applications involve hyperbolic systems of conservation laws with source terms. The numerical solution of such systems may be challenging, especially when the source terms are stiff. Uniform accuracy with respect to the stiffness parameter is a highly desirable property but it is, in general, very difficult to achieve using underresolved discretizations. For such problems we develop different second order uniformly accurate high-resolution nonoscillatory central schemes. The schemes retain the simplicity of central schemes for hyperbolic conservation laws and avoid the use of Riemann solvers. In particular, we show that these schemes possess a discrete analogue of the continuous asymptotic limit and are able to capture the correct behavior even if the initial layer and the small relaxation time are not numerically resolved.