Boundary integral solution method for diffusion-reaction problems with both material and rate nonlinearities (Q1174524)

This paper is concerned with the diffusion-reaction problems with both material and rate nonlinearity \({d\over dx}(D[c]{dc\over dx}) = f[c]\) \((0 < x < 1)\) subject to the mixed boundary conditions at both end points. Here the bracket denotes the functional dependency. Over a subinterval of \([0,1]\), \(f[c]\) is first approximated by \(k_ 1 + k_ 2c\). Second, the weighted weak formulation leads to the integral form of the problem. The weighting functions are derived from the simple solutions for \({d^ 2G\over dx^ 2} = 0\) and \(dG{d\over x} = 0\). Further, the osculating polynomial equation for \(c\) yields the equation for the numerical solution. Test examples with numerical results are given. However, there is no discussion of the convergence or accuracy.