Strict stability of high-order compact implicit finite-difference schemes: The role of boundary conditions for hyperbolic PDEs. II (Q1979127)

This is an extension of part I [ibid. 160, No. 1, 42-66 (2000; reviewed above)] on high order implict finite difference schemes for a linear hyperbolic initial boundary value problem. This paper contains two parts. The first part of the paper is devoted to the proof of the time stability of the schemes. The time stabilities of the 6th and 4th order schemes in one dimension are estabilished under the conditions \(\|L\|\cdot \|R\|\leq 1/\) and \(\|L\|\cdot \|R\|\leq 1/3\), respectively. However, numerical results show that these conditions are not necessary. In the second part of the paper the authors discuss the application of the method to the 2D Maxwell equations. Numerical results using the Maxwell equations are presented and compared with some existing ones.