Power-series method for two-dimensional heat conduction problems

The power-series method, i.e., a new finite analytic approach based on power-series expansion, is applied to two-dimensional heat conduction problems and the solutions are compared with those obtained with finite-difference techniques such as the Barakat-Clark, Crank-Nicolson, and fully implicit methods. A comparison with uniform-grid systems reveals that the power-series scheme yields more accurate solutions to a wide range of time steps than the finite-difference methods. A comparison with nonuniform-grid systems shows that this method yields the most accurate solutions. The stability of the power-series method is also evaluated.