The simple, explicit difference method for transient heat conduction problems

1 The simple, explicit difference method for transient heat conduction problems 

In the finite difference method, the derivatives dfl/dt, dfl/dx and d2d/dx2, which appear in the heat conduction equation and the boundary conditions, are replaced by difference quotients. This discretisation transforms the differential equation into a finite difference equation whose solution approximates the solution of the differential equation at discrete points which form a grid in space and time. A reduction in the mesh size increases the number of grid points and therefore the accuracy of the approximation, although this does of course increase the computation demands. Applying a finite difference method one has therefore to make a compromise between accuracy and computation time. 

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