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The stability of the Crank Nicolson scheme for the numerical solution of the heat conduction equation subject to separated boundary conditions is demonstrated. This result is extended to separable equations with variable coefficients and to the heat conduction equation in cylindrical geometry which has a singular coefficient. The solution of the difference approximation to the heat conduction equation is shown to reflect accurately the pattern of behaviour of the differential equation, and thisdoi:10.1093/comjnl/12.1.82 fatcat:snmcwq4ccrgnvomwt3qurzhvgq