Pseudospectral methods for computing the multiple solutions of the LaneEmden equation ?
Based on the LiapunovSchmidt reduction and symmetry-breaking bifurcation theory, we compute and visualize multiple solutions of the LaneEmden equation on a square and a disc, using Legendre and FourierLegendre pseudospectral methods. Starting from the nontrivial solution branches of the corresponding nonlinear bifurcation problem, we obtain multiple solutions of LaneEmden equation with various symmetries numerically. Numerical results demonstrate the effectiveness of these approaches.
pseudospectral method multiple solutions laneemden equation liapunovschmidt reduction symmetry-breaking bifurcation theory