A novel spectral method for Burgers equation on the real line. (English) Zbl 1468.65164
Summary: A spectral method for the Burgers equation on the whole real line based on generalised Hermite functions is proposed. The generalised stability and convergence of the method are proved. Numerical results confirm the theoretical findings and demonstrate the efficiency of the algorithm.
MSC:
| 65M70 | Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs |
| 65L06 | Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations |
| 65M12 | Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs |
| 41A30 | Approximation by other special function classes |
| 33C45 | Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) |
| 76M22 | Spectral methods applied to problems in fluid mechanics |
| 35Q35 | PDEs in connection with fluid mechanics |
Keywords:
Burger equation on the real line; spectral method; nonlinear problem; generalised Hermite functionReferences:
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