SIAM Journal on Numerical Analysis
Summation by parts for finite difference approximations for d/dx
Journal of Computational Physics
Stiffness in numerical initial-value problems
Journal of Computational and Applied Mathematics
A stable and conservative interface treatment of arbitrary spatial accuracy
Journal of Computational Physics
Journal of Computational and Applied Mathematics - Special issue on numerical anaylsis 2000 Vol. VI: Ordinary differential equations and integral equations
Journal of Scientific Computing
Additive Runge-Kutta schemes for convection-diffusion-reaction equations
Applied Numerical Mathematics
On Coordinate Transformations for Summation-by-Parts Operators
Journal of Scientific Computing
Summation by parts operators for finite difference approximations of second derivatives
Journal of Computational Physics
Fourth-Order Runge---Kutta Schemes for Fluid Mechanics Applications
Journal of Scientific Computing
Journal of Scientific Computing
Journal of Computational Physics
Application of implicit-explicit high order Runge-Kutta methods to discontinuous-Galerkin schemes
Journal of Computational Physics
IMEX extensions of linear multistep methods with general monotonicity and boundedness properties
Journal of Computational Physics
Error Bounded Schemes for Time-dependent Hyperbolic Problems
SIAM Journal on Scientific Computing
A stable high-order finite difference scheme for the compressible Navier-Stokes equations
Journal of Computational Physics
A stable and conservative high order multi-block method for the compressible Navier-Stokes equations
Journal of Computational Physics
A stable and high-order accurate conjugate heat transfer problem
Journal of Computational Physics
Stable Robin solid wall boundary conditions for the Navier-Stokes equations
Journal of Computational Physics
Superconvergent Functional Estimates from Summation-By-Parts Finite-Difference Discretizations
SIAM Journal on Scientific Computing
Stepsize Restrictions for Boundedness and Monotonicity of Multistep Methods
Journal of Scientific Computing
Verification of variable-density flow solvers using manufactured solutions
Journal of Computational Physics
Journal of Computational Physics
Journal of Scientific Computing
Journal of Computational Physics
On the impact of boundary conditions on dual consistent finite difference discretizations
Journal of Computational Physics
Journal of Scientific Computing
Hi-index | 31.45 |
We develop a new high order accurate time-integration technique for initial value problems. We focus on problems that originate from a space approximation using high order finite difference methods on summation-by-parts form with weak boundary conditions, and extend that technique to the time-domain. The new time-integration method is global, high order accurate, unconditionally stable and together with the approximation in space, it generates optimally sharp fully discrete energy estimates. In particular, it is shown how stable fully discrete high order accurate approximations of the Maxwells' equations, the elastic wave equations and the linearized Euler and Navier-Stokes equations can obtained. Even though we focus on finite difference approximations, we stress that the methodology is completely general and suitable for all semi-discrete energy-stable approximations. Numerical experiments show that the new technique is very accurate and has limited order reduction for stiff problems.