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Chebyshev pseudospectral approximation of two dimensional fractional Schrodinger equation on a convex and rectangular domain
- Source :
- AIMS Mathematics, Vol 5, Iss 3, Pp 1642-1662 (2020)
- Publication Year :
- 2020
- Publisher :
- AIMS Press, 2020.
-
Abstract
- In this article, the authors report the Chebyshev pseudospectral method for solving twodimensional nonlinear Schrodinger equation with fractional order derivative in time and space both. The modified Riemann-Liouville fractional derivatives are used to define the new fractional derivatives matrix at CGL points. Using the Chebyshev fractional derivatives matrices, the given problem is reduced to a diagonally block system of nonlinear algebraic equations, which will be solved using Newton's Raphson method. The proposed methods have shown error analysis without any dependency on time and space step restrictions. Some model examples of the equations, defined on a convex and rectangular domain, have tested with various values of fractional order α and β. Moreover, numerical solutions are demonstrated to justify the theoretical results.
- Subjects :
- nonlinear fractional schrodinger equation (nfse)
modified riemann-liouville fractional derivatives
General Mathematics
lcsh:Mathematics
pseudospectral method
chebyshev-gauss-lobbato points
lcsh:QA1-939
Chebyshev filter
Fractional calculus
Nonlinear system
Algebraic equation
symbols.namesake
Matrix (mathematics)
Chebyshev pseudospectral method
symbols
Applied mathematics
Pseudo-spectral method
Nonlinear Schrödinger equation
error analysis
Mathematics
Subjects
Details
- Language :
- English
- ISSN :
- 24736988
- Volume :
- 5
- Issue :
- 3
- Database :
- OpenAIRE
- Journal :
- AIMS Mathematics
- Accession number :
- edsair.doi.dedup.....16cff26b9f371f937f8d8f194886e686