The finite difference method (FDM)#

The partial differential equations (PDEs) that govern important natural processes and that we need to solve to obtain societal and economic benefits are, in the most cases, impossible to solve analitically. Therefore we must think on solving them numerically.

Solving a PDE numerically means that we replace the analytical manipulation of the derivatives with algebraic manipulations which, in addition, opens up the possibility of using computers in the process. This possibility has enabled the spectacular progress in fields such as numerical weather prediction that has radically changed our lives and wouldn’t be possible without the use of computers.