Geodesic
Time step selection for the numerical solution of boundary value problems for parabolic equations
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 57 (2017) no. 5, pp. 842-853

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An algorithm is proposed for selecting a time step for the numerical solution of boundary value problems for parabolic equations. The solution is found by applying unconditionally stable implicit schemes, while the time step is selected using the solution produced by an explicit scheme. Explicit computational formulas are based on truncation error estimation at a new time level. Numerical results for a model parabolic boundary value problem are presented, which demonstrate the performance of the time step selection algorithm. 
@article{ZVMMF_2017_57_5_a6,
     author = {P. N. Vabishchevich and A. O. Vasil'ev},
     title = {Time step selection for the numerical solution of boundary value problems for parabolic equations},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {842--853},
     publisher = {mathdoc},
     volume = {57},
     number = {5},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2017_57_5_a6/}
}
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P. N. Vabishchevich; A. O. Vasil'ev. Time step selection for the numerical solution of boundary value problems for parabolic equations. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 57 (2017) no. 5, pp. 842-853. http://geodesic.mathdoc.fr/item/ZVMMF_2017_57_5_a6/