Abstract
This paper studies the use of ADE methods for solving diffusion equations in non-Cartesian coordinates. To retain unconditional stability and greater accuracy of computation when solving diffusion equations in non-Cartesian coordinates, a new explicit algorithm is developed by combining the advantages of those originally proposed by Saul’ev, Larkin, Barakat and Clark. Analysis of accuracy shows that the new algorithm can be as accurate as either that of Larkin or that of Barakat and Clark. Stability analysis is also carried out “locally” based on the spectral stability, and this shows unconditional stability of the generalised algorithm. Numerical examples on transient heat conduction are used to support the conclusions from the analysis.
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