In this work a computer simulation of impurity diffusion in the vicinity of individual bicrystalline grain boundary has been carried out with the use of a modified Fisher model in which the grain's boundary influence (in the form of internal mechanical stresses) onto impurity atoms is taken into account. In computations the monotone difference schemes of the second order of accuracy on irregular grids were used. For such schemes under intrinsic restrictions on the grid steps the stability in the uniform norm has been proved.
Chuiko, M. M., Fedotov, A., & Rychagov, V. G. (1998). Mathematical modelling of impurity diffusion in grain boundary neighborhood in a dislocation wall force field (modified fisher model). Mathematical Modelling and Analysis, 3(1), 57-67. https://doi.org/10.3846/13926292.1998.9637086
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