| The numerical solution of one-dimensional heat conduction equation in unbounded domain is considered. An artificial boundary is introduced to make the computational domain finite and an exact artificial boundary condition is employed to reduce the original problem into an initial-boundary value problem, which is then discretized by applying the Crank-Nicolson scheme in time variable and linear or quadratic finite element method in spatial variable, respectively. The overall sheme, by a rigorous theoretial analysis, is proved to be unconditionally stable and convergent, the global error order is also obtained.
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