Mastering Python for Finance - Second Edition

The implicit method

The instability problem of the explicit method can be overcome using the forward difference with respect to time. The implicit method for approximating f_i,j is given by the following equation:

Here, it can be seen that the only difference between the implicit and explicit approximating scheme lies in the first difference, where the forward difference with respect to t is used in the implicit scheme. When we rearrange the terms, we get the following expression:

Where:

Here:

The iterative approach of the implicit ...