5 Accelerated Development of Implicit Methods Using Tools for Scientific Computing

Abstract

The Euler, Navier-Stokes, and similar equations can be used to describe a wide variety of physical phenomena. Thus, the accurate and efficient solution of these equations is important to many applications. However, because of the difficulty involved in implementing an implicit method by hand, the solution is often determined using an explicit method. We describe how an existing explicit solver can be combined with readily available tools for scientific computing to develop an effective implicit method very rapidly. This method can offer improvement by an order of magnitude or more over an explicit multi-step Runge-Kutta method.