Exponential Integration for System of Linear Ordinary Differential Equations

Author: Tamari Janelidze
Keywords: Exponential Integration, Magnus, ODE
Annotation:

Linear system of differential equations with varying coefficients is widely used by a number of scientific and engineering areas. In this work first an introduction of ordinary differential equations is presented. The main idea how to solve first order scalar equation or system of linear equations is described. Then Magnus integrator is is considered to solve linear, non-constant coefficient system of ordinary differential equations, that generalizes standard technique of solving first-order scalar linear ODEs. Traditional Magnus integrator as well as recently developed commutator-free Magnus integrators are considered.