A convergence analysis of hopscotch methods for fourth order parabolic equations (Q1085962)

The authors consider the recursion \((I+C)U_{n+1}=BU_ n+(I+C)U_{n- 1}\) arising when a hopscotch method is applied to a fourth-order parabolic equation. The matrices B, C are real skew-Hermitian. A condition for the method to be stable is derived. It is not clear whether this condition is best possible or whether it holds when the coefficients of the original problem vary in space and time. In fact the well-known energy method yields all this information.