Analytical approximate solutions of certain nonlinear equations of reaction-diffusion kind (Q1179097)

The authors treat the numerical solution of initial-boundary value problems for reaction-diffusion systems of the form \(\hbox{div}(D(X)\nabla c)-k^ 2G(X)c=0\), \(X_ t=G(X)_ c\) using the method of ``monotone transformations'' in which a sequence of approximate solutions \((c_ i,X_ i)\) is built up on the basis of exact solutions of approximate problems. These problems are obtained by approximation of \(D\) and \(G\). Error bounds and numerical results are given.