A numerical technique of the time fractional gas dynamics equation using finite element approach with cubic Hermite element. (A numerical technique of the time fractional gas dynamics equation using finite element approach with cubic Hermit element.) (English) Zbl 1533.65182
Summary: In this paper, a numerical scheme solution of the non-linear time fractional gas dynamics model using finite element method is proposed. In this regard, cubic Hermite element has been used. Caputo-type derivative has been used for describing the temporal fractional derivative in the equation. In this occasion, the \(L^1\) discretization tool is applied to the time term in the equation. For the reliability, the error norms \(L^2\) and \(L^\infty\) have been calculated. The findings of this work are found to be in good agreement with the exact solutions. Comparisons are made with those of some previous related works.
MSC:
| 65M60 | Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs |
| 65M06 | Finite difference methods for initial value and initial-boundary value problems involving PDEs |
| 65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |
| 33C45 | Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) |
| 65R10 | Numerical methods for integral transforms |
| 76N15 | Gas dynamics (general theory) |
| 26A33 | Fractional derivatives and integrals |
| 35R11 | Fractional partial differential equations |
| 35Q35 | PDEs in connection with fluid mechanics |
