Solving Linear Algebraic and Differential Equations with L-Systems

In the previous note it was shown how L-Systems can be used to numerically solve systems of partial differential equations, for a constant or growing medium, and the method was applied to computer graphics purposes. The LSystem from the previous section employed a forward Euler method for finite differencing. Although simple to implement, the forward Euler method is in many case inadequate, for example when the equations are stiff. In this note we show how an implicit method for solving differential equations can be implemented within the framework of L-Systems. At the heart of this method lies a technique for solving systems of banded linear equations. To present this method, we use analogy between the processes involved in diffusion and the behavior of electric circuits.