Abstract
The matrix stability of the backward differentiation formula (BDF) algorithm for the numerical solution of the reaction–diffusion partial differential equations arising in electrochemistry, as a function of the number of time levels k and under several boundary conditions, was studied. The study included also the two-species catalytic mechanism, and unequal intervals (nonuniform spatial grid). The method is unconditionally stable in all cases for k⩽7 (that is, order ⩽6) irrespective of the rate of homogeneous chemical reactions or boundary conditions. Homogeneous chemical reactions, except in the case of the two-species catalytic reaction, were found to have a stabilising effect.
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