Computation of non-smooth local centre manifolds

^** Email: msjolly{at}indiana.edu^*** Email: rrosa{at}ufrj.br An iterative Lyapunov–Perron algorithm for the computationof inertial manifolds is adapted for centre manifolds and appliedto two test problems. The first application is to compute aknown non-smooth manifold (once, but not twice differentiable),where a Taylor expansion is not possible. The second is to asmooth manifold arising in a porous medium problem, where rigorouserror estimates are compared to both the correction at eachiteration and the addition of each coefficient in a Taylor expansion.While in each case the manifold is 1D, the algorithm is well-suitedfor higher dimensional manifolds. In fact, the computationalcomplexity of the algorithm is independent of the dimension,as it computes individual points on the manifold independentlyby discretising the solution through them. Summations in thealgorithm are reformulated to be recursive. This accelerationapplies to the special case of inertial manifolds as well.