Strict stability of high-order compact implicit finite-difference schemes: The role of boundary conditions for hyperbolic PDEs. I
The authors construct and analyze a class of high order finite difference schemes for a linear hyperbolic initial boundary value problem in one and two dimensions. The spatial discretization is based on an implicit and compact finite difference approximation to the first derivative constructed on a uniform partition. Two Toeplitz matrices are used in the construction of the approximation. It is proved that the method is strictly stable, and the error bound is essentially governed by the truncation error of the finite difference approximation. An existing technique, called SAT procedure, is borrowed and modified to handle the boundary approximation which does not affect the overall approximation accuracy. Various numerical examples are solved to confirm the theoretical results obtained. [For part II see ibid. 160, No. 1, 67-87 (2000; reviewed below)].
linear hyperbolic initial boundary value problem
scientific article; zbMATH DE number 1452588
scientific article