A modified equation approach to constructing fourth order methods for acoustic wave propagation
SIAM Journal on Scientific and Statistical Computing
SIAM Journal on Numerical Analysis
SIAM Journal on Numerical Analysis
Journal of Computational Physics
Difference Approximations for the Second Order Wave Equation
SIAM Journal on Numerical Analysis
On Coordinate Transformations for Summation-by-Parts Operators
Journal of Scientific Computing
Stable and Accurate Artificial Dissipation
Journal of Scientific Computing
Summation by parts operators for finite difference approximations of second derivatives
Journal of Computational Physics
Time Compact Difference Methods for Wave Propagation in Discontinuous Media
SIAM Journal on Scientific Computing
Steady-State Computations Using Summation-by-Parts Operators
Journal of Scientific Computing
On the order of accuracy for difference approximations of initial-boundary value problems
Journal of Computational Physics
Interior penalty discontinuous Galerkin method for Maxwell's equations: Energy norm error estimates
Journal of Computational and Applied Mathematics
Journal of Computational Physics
Stable and accurate schemes for the compressible Navier-Stokes equations
Journal of Computational Physics
A stable high-order finite difference scheme for the compressible Navier-Stokes equations
Journal of Computational Physics
Stable and accurate wave-propagation in discontinuous media
Journal of Computational Physics
SIAM Journal on Scientific Computing
Stable and Accurate Interpolation Operators for High-Order Multiblock Finite Difference Methods
SIAM Journal on Scientific Computing
Journal of Computational Physics
On the impact of boundary conditions on dual consistent finite difference discretizations
Journal of Computational Physics
High-order entropy stable finite difference schemes for nonlinear conservation laws: Finite domains
Journal of Computational Physics
High-order accurate difference schemes for the Hodgkin-Huxley equations
Journal of Computational Physics
Dual consistency and functional accuracy: a finite-difference perspective
Journal of Computational Physics
A perfectly matched layer for the time-dependent wave equation in heterogeneous and layered media
Journal of Computational Physics
Journal of Computational Physics
Optimal diagonal-norm SBP operators
Journal of Computational Physics
A generalized framework for nodal first derivative summation-by-parts operators
Journal of Computational Physics
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Finite difference operators approximating second derivatives with variable coefficients and satisfying a summation-by-parts rule have been derived for the second-, fourth- and sixth-order case by using the symbolic mathematics software Maple. The operators are based on the same norms as the corresponding approximations of the first derivative, which makes the construction of stable approximations to general multi-dimensional hyperbolic-parabolic problems straightforward.