A low cost Arnoldi method for large linear initial value problems

Abstract

In this article, we introduce a low cost method for integrating large dimensional linear initial value problems based on the Arnoldi algorithm for matrix functions. We also describe a very efficient step-size control technique and compare a resulting algorithm of order 4 with the standard Matlab solvers on linear stiff problems arising from the discretization of parabolic equations.

Keywords:

• Exponential integrators
• Krylov methods
• Arnold method
• Linear stiff problems
• Matrix functions