Method of lines

The method of lines (MOL, NMOL, NUMOL[1][2][3]) is a technique for solving partial differential equations (PDEs) in which all but one dimension is discretized.

Many integration routines have been developed over the years in many different programming languages, and some have been published as open source resources.

[5] Many papers discussing the accuracy and stability of the method of lines for various types of partial differential equations have appeared since.

Finite differences are then used to approximate the spatial derivatives, and the resulting system of equations is solved by MOL.

[9] In this method, the discretization process results in a set of ODE's that are solved by exploiting properties of the associated exponential matrix.