Modified Legendre rational spectral method for Burgers equation on the whole line. (English) Zbl 1538.65432
Summary: In this paper, we propose a spectral method for the Burgers equation using the modified Legendre rational functions, and prove its generalized stability and convergence. Numerical results demonstrate the efficiency of the new approach.
MSC:
| 65M70 | Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs |
| 41A30 | Approximation by other special function classes |
| 76M22 | Spectral methods applied to problems in fluid mechanics |
| 33C45 | Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) |
| 65M12 | Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs |
Keywords:
Burgers equation; spectral method; modified Legendre rational functions; problem on the whole lineReferences:
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