A reaction–diffusion system arising from electrochemistry

This work is concerned with a reaction–diffusion system in cylindrical coordinates that arises from electrochemistry. A Laplace transform solution for the current density is found to have two branch points and is inverted by a suitable Bromwich contour, with the solution taking the form of the sum of two integrals; in a special case, one of the integrals reduces to the Jaeger integral, ℐ(0,1;t). A treatment of the highly accurate computation of these two integrals by a C++ code, using exclusively extended precision variables, is given. The solution of the equivalent problem in Cartesian coordinates is also supplied in the form of two integrals.