A six-stage third order additive method for stiff ordinary differential equations
For researchers solving stiff ODEs, this provides a new method with practical stepsize control, though it is an incremental improvement over existing additive methods.
The authors developed a third-order additive method for stiff ODEs that is L-stable for the implicit part and allows arbitrary Jacobian approximations, with automatic stepsize control. Numerical experiments demonstrated reliability and efficiency.
In this paper we construct a third order method for solving additively split autonomous stiff systems of ordinary differential equations. The constructed additive method is L-stable with respect to the implicit part and allows to use an arbitrary approximation of the Jacobian matrix. Automatic stepsize selection based on local error and stability control are performed. The estimations for error and stability control have been obtained without significant additional computational costs. Numerical experiments show reliability and efficiency of the implemented integration algorithm.