On the decomposition method to the heat equation with non‐linear and non‐local boundary conditions

Abstract

The Adomian decomposition method is used and applied to the mathematical model of a biosensor. This model consists of a heat equation with non‐linear and non‐local boundary conditions. To obtain a canonical form of Adomian, an equivalent non‐linear Volterra integral equation with a weakly singular kernel is set up. In addition, the asymptotic behaviour of the solution as t → 0 and t → • by asymptotic decomposition is obtained. Finally, numerical results are given which support the theoretical results.

Citation

Hadizadeh, M. and Maleknejad, K. (1998), "On the decomposition method to the heat equation with non‐linear and non‐local boundary conditions", Kybernetes, Vol. 27 No. 4, pp. 426-434. https://doi.org/10.1108/03684929810219431