A non-homogeneous method of third order for additive stiff systems of ordinary differential equations
This work offers a more efficient integration algorithm for solving additive stiff ODEs, which is relevant for computational scientists dealing with stiff systems.
The paper presents a third-order additive method for stiff ODEs that is L-stable for the implicit part and uses an explicit fourth stage to reduce computational cost. Numerical experiments confirm the method's 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. In opposite to our previous paper, the fourth stage is explicit. So, the constructed method also has a good stability properties because of L-stability of the intermediate numerical formulas in the fourth stage, but has a lower computational costs per step. 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.