Jacobian-free Locally Linearized Runge-Kutta method of Dormand and Prince for large systems of differential equations
This Matlab toolbox provides the two implementations of the Jacobian-free Locally Linearized Runge-Kutta method of Dormand and Prince (LLDP) described in [1] for the integration of large systems of initial value problems.
[1] Jacobian-free Locally Linearized Runge-Kutta method of Dormand and Prince for large systems of differential equations by F.S. Naranjo-Noda and J.C. Jimenez
LLDP1
variable step-size Jacobian-free Locally Linearized Runge-Kutta method of Dormand and Prince with variable order finite difference in the Arnoldi algorithm
LLDP2
variable step-size Jacobian-free Locally Linearized Runge-Kutta method of Dormand and Prince with fixed order 1 finite difference in the Arnoldi algorithm
run_examples_lldp_fj.m
generates the Tables 3-5 of [1] illustrating the performance of the Jacobian-free Locally Linearized Runge-Kutta method of Dormand and Prince schemes LLDP1 and LLDP2 in the integration of test examples.
run_large_examples_lldp_fj.m
generates the Table 7 of [1] illustrating the performance of the Jacobian-free Locally Linearized Runge-Kutta method of Dormand and Prince schemes LLDP1 and LLDP2 in the integration of test examples with larger dimensions.