Explicit Method For Heat Conduction Equations

Explicit method : Explicit method is used in numerical analysis for determining the time dependent ordinary and partial differentiation.

Let us consider the Equation,

...................1.1

Now, use the approximation,

.....................1.2

Using central differences, we also have the approximation,

......................1.3

Therefore, an approximation to the heat conduction equation 

at the point (x_i , t_{j 1}), is

or,

or,

or,

 

where λ = kc₂/h₂, is called the mesh ratio parameter.

Note that the value ui, j 1 at the node (x_i, t_{j 1}) is being obtained explicitly using the values on the previous time level t_j . The nodes that are used in the computations are given in Fig.1.1. This method is called the Schmidt method. It is a two level method.

figure :Schmidt method.