AbstractA new algorithm for eigenvalue problems for linear differential operators with fractional derivatives is proposed and justified.
The algorithm is based on the approximation (perturbation) of the coefficients of a part of the differential operator by piecewise constant functions where the eigenvalue problem for the last one is supposed to be simpler than the original one. Another milestone of the algorithm is the homotopy idea which results at the possibility for a given eigenpair number to compute recursively a sequence of the approximate eigenpairs. This sequence converges to the exact eigenpair with a super-exponential convergence rate. The eigenpairs can be computed in parallel for all prescribed indexes. The proposed method possesses the following principal property: its convergence rate increases together with the index of the eigenpair.
Numerical examples confirm the theory.
Fokas Diagonalization of Piecewise Constant Coefficient Linear Differential Operators on Finite Intervals and Networks
