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The power-series method, i.e., a new finite analytic approach based on power-series expansion, was applied to one-dimensional heat-conduction problems to study its stability and accuracy. The stability of this method for non-uniform grid systems is confirmed numerically within a range where 10-5<Δt, ΔχE, ΔχW, and a<105 and 10-5<β<105. The solutions of the present method were compared with the fully implicit and Stefanovic-Stephan methods. A comparison with non-uniform-grid systems showed that this method yielded accurate and robust solutions.

Stability and Accuracy of Power-series Method (In Case of One-dimensional Heat Conduction)