fsadannn / HOLLmethods

High Order Local Linearization methods

This repo hold the original source code used for the Local Linearization papers

This Matlab toolbox provides the Jacobian-free High Order Local Linearization (HOLL) schemes JFLLRK and JFLLRK4 described in [1] for the integration of large systems of initial value problems.

[1] Jacobian-free High Order Local Linearization methods for large systems of initial value problems by F.S. Naranjo-Noda and J.C. Jimenez

Jacobian-free HOLL

JFLLRK4 fixed step-size Jacobian-free Locally Linearized Runge-Kuttta scheme of order 4

JFLLRK fixed step-size Jacobian-free Locally Linearized Runge-Kuttta scheme with variable parameters

Demos

run_examples.m generates the Tables 5-8 of [1] illustrating the performance of the Jacobian-free HOLL scheme JFLLRK4 in the integration of test examples.

run_convergence.m generates the Figures 1-3 and Tables 2-4 of [1] illustrating the convergence rate of the Jacobian-free HOLL scheme JFLLRK for different parameter values.