Accurate Spectral Collocation Solutions to 2nd-Order Sturm–Liouville Problems

This work is about the use of some classical spectral collocation methods as well with new software system Chebfun in order to compute eigenpairs high Sturm–Liouville eigenproblems. The analysis divided into two distinct directions. For problems clamped boundary conditions, we preconditioning differentiation matrices and for hinged end conditions equation transformed a second then conventional ChC applied. A challenging set “hard” benchmark problems, which usual numerical (FD, FE, shooting, etc.) encounter difficulties or even fail, are analyzed evaluate qualities drawbacks methods. In separate “good” “bad” (spurious) eigenvalues, estimate drift eigenvalues interest respect approximation N. gives us very precise indication accuracy computed, i.e., an automatic estimation error control eigenvalue error. Two MATLAB codes models (ChC SiC) another provided. They outperform old used so far can be easily modified solve other problems.