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

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 --> infinity by asymptotic decomposition is obtained. Finally, numerical results are given which support the theoretical results.