A fully diagonalized spectral method using generalized Laguerre functions on the half line. (English) Zbl 1387.76077
Summary: A fully diagonalized spectral method using generalized Laguerre functions is proposed and analyzed for solving elliptic equations on the half line. We first define the generalized Laguerre functions which are complete and mutually orthogonal with respect to an equivalent Sobolev inner product. Then the Fourier-like Sobolev orthogonal basis functions are constructed for the diagonalized Laguerre spectral method of elliptic equations. Besides, a unified orthogonal Laguerre projection is established for various elliptic equations. On the basis of this orthogonal Laguerre projection, we obtain optimal error estimates of the fully diagonalized Laguerre spectral method for both Dirichlet and Robin boundary value problems. Finally, numerical experiments, which are in agreement with the theoretical analysis, demonstrate the effectiveness and the spectral accuracy of our diagonalized method.
MSC:
| 76M22 | Spectral methods applied to problems in fluid mechanics |
| 33C45 | Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) |
| 35J25 | Boundary value problems for second-order elliptic equations |
| 65L70 | Error bounds for numerical methods for ordinary differential equations |
Keywords:
spectral method; Sobolev orthogonal Laguerre functions; elliptic boundary value problems; error estimatesReferences:
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