HIGHER ORDER ACCURATE PARTIAL IMPLICITIZATION:AN UNCONDITIONALLY STABLE FOURTH-ORDER-ACCURATE EXPLICIT NUMERICAL TECHNIQUE

摘要

An unconditionally stable fourth-order-accurate explicit numerical technique is derived, based on the method of partial implicitization. The Von Neumann stability analysis demonstrates the unconditional linear stability. The order of the truncation error is deduced from the Taylor series expansions of the linearized difference equations and is verified by numerical solutions to Burgers' equation. For comparison, results are also presented for Burgers' equation using a second-order-accurate partial-implicitization scheme, as well as the fourth-order scheme of Kreiss.