Abstract
In this paper the parallel difference schemes with variable time steplengths for heat equations are studied. The absolute stability of the constructed schemes are proved. The numerical results of the alternating segment explicit-implicit (ASE-I) scheme and the alternating group explicit (AGE) scheme are presented. They show that the variable time steplength scheme provides good approximate solution that is more accurate than the solution of the equal time steplength scheme, and the former can be obtained with less computational effort than the latter.
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