Crank-Nicolson implicit algorithm

There are a number of numerical algorithms to solve the difference equation representation of the partial differential equations. Implicit algorithms such as Crank-Nicolson scheme where the finite difference representations for the spatial derivatives are averaged over two successive times, t = nAt and t = n + l)At, are frequently used because they are usually unconditionally stable algorithms. Most conservation laws lead to equations of the form... 

CN Crank-Nicolson without the implicit boundary algorithm ... 

Bieniasz LK, 0steiby O, Blitz D (1995) Numerical stability of finite difference algorithms for electrochemical kinetic simulations matrix stability analysis of the classic explicit, fully implicit and Crank-Nicolson methods and typical problems involving mixed boundtiry conditions. Comput Chem 19 121-136... 

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