A finite‐difference method of high‐order accuracy for the solution of three‐dimensional transient heat conduction problems

Abstract

Abstract A finite‐difference method is presented for solving three‐dimensional transient heat conduction problems. The method is a modification of the method of Douglas and Rachford which achieves the higher‐order accuracy of a Crank‐Nicholson formulation while preserving the advantages of the Douglas‐Rachford method: unconditional stability and simplicity of solving the equations at each time level. Although the method has not yet been applied, the analysis in this paper suggests that it will prove to be the most efficient method yet proposed for the numerical integration of three‐dimensional transient heat conduction problems.