Müntz pseudo-spectral method: theory and numerical experiments. (English) Zbl 1453.65358
Summary: This paper presents two new non-classical Lagrange basis functions which are based on the new Jacobi-Müntz functions presented by the authors recently. These basis functions are, in fact, generalized forms of the newly generated Jacobi-based functions. With respect to these non-classical Lagrange basis functions, two non-classical interpolants are introduced and their error bounds are proved in detail. The pseudo-spectral differentiation (and integration) matrices have been extracted in two different manners. Some numerical experiments are provided to show the efficiency and capability of these newly generated non-classical Lagrange basis functions.
MSC:
| 65M70 | Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs |
| 26A33 | Fractional derivatives and integrals |
| 33C45 | Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) |
| 58C40 | Spectral theory; eigenvalue problems on manifolds |
| 65M15 | Error bounds for initial value and initial-boundary value problems involving PDEs |
| 35R11 | Fractional partial differential equations |
| 34A08 | Fractional ordinary differential equations |
Keywords:
non-classical interpolants; orthogonal projections; error bounds; fractional ordinary and partial differential equationsSoftware:
MatlabReferences:
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