Summary: Many physical phenomena are modelled by non-classical parabolic boundary value problems with non-local boundary conditions. In [M. Dehghan
, Appl. Numer. Math. 52, No. 1, 39–62 (2005; Zbl 1063.65079
)], several methods were compared to approach the numerical solution of the one-dimensional heat equation subject to specifications of mass. One of them was the (3,3) Crandall formula. The scheme displayed in Eq. (64) in that paper is of order
, not of order
as proposed by that author. However, it is possible with several changes to derive a Crandall algorithm of order
. Here, we compare the efficiency of the new method with the previous results in the same tests, and we reach errors
times smaller with the new scheme.