Numerical solution of heat conduction problems

Douglas, J. Rachford, H.H. On the numerical solution of heat conduction problems in two and three space variables. Trans. Amer. Math. Soc. 82 (1956) 421-439... 

Generally, the Crank-Nicolson method is used for numerical solution of heat conduction problems that are parabolic in nature. This method solves a mesh with mesh size h in x-direction and mesh size k in y-direction (time direction). It calculates the values of u at six points as shown in Figure 1.17. 

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