Explicit and Implicit Methods for Two-Dimensional Heat Conduction Equation

The two-dimensional conduction is given by

(5.5)

Here, the dependent variable, (temperature) is a function of space and ( )and () is the thermal diffusivity.

If we apply the simple explicit method to heat conduction equation, the following algorithm results

(5.6)

When we apply the crank-Nicolson to the two-dimensional heat conduction equation, we obtain

(5.7)

where the central difference operators and in two different spatial directions are defined by

	(5.8)