Inverse power method for the principal eigenvalue of the Robin p-Laplacian

In this paper, a numerical algorithm to compute the first eigenvalue and the corresponding eigenfunction of the p-Laplacian eigenvalue problem with Robin boundary conditions is developed. The algorithm generates a sequence of numbers and functions. It is established that the sequence of numbers is decreasing and converges to the first eigenvalue, while the sequence of functions converges to the corresponding eigenfunction. The method is easier to implement in comparison with the current methods.The order of convergence for the algorithm is investigated. Several numerical experiments reveal the robustness and the efficacy of the algorithm for domains of various geometries. Our results provide deeper insights for the limiting cases p→1 and ∞.