Solving differential eigenproblems via the spectral Tau method. (English) Zbl 07676502
Summary: The spectral Tau method to compute eigenpairs of ordinary differential equations is implemented as part of the Tau Toolbox – a numerical library for the solution of integro-differential problems. This mathematical software enables a symbolic syntax to be applied to objects to manipulate and solve differential problems with ease and accuracy. The library is explained in detail and its application to various problems is illustrated: numerical approximations for linear, quadratic, and nonlinear differential eigenvalue problems.
MSC:
| 65L15 | Numerical solution of eigenvalue problems involving ordinary differential equations |
| 65L60 | Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations |
| 65F15 | Numerical computation of eigenvalues and eigenvectors of matrices |
| 33C45 | Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) |
| 34B24 | Sturm-Liouville theory |
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