Geodesic
Approximation of Hamilton-Jacobi Equations with the Caputo Time-Fractional Derivative
Minimax theory and its applications, Tome 5 (2020) no. 2
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We investigate the numerical approximation of Hamilton-Jacobi equations with the Caputo time-fractional derivative. We introduce an explicit in time discretization of the Caputo derivative and a finite difference scheme for the approximation of the Hamiltonian. We show that the approximation scheme so obtained is stable under an appropriate condition on the discretization parameters and converges to the unique viscosity solution of the Hamilton-Jacobi equation.
Mots-clés : Fractional Hamilton-Jacobi equation, Caputo time derivative, finite difference, convergence 
@article{MTA_2020_5_2_a2,
     author = {Fabio Camilli,Serikbolsyn Duisembay},
     title = {Approximation of {Hamilton-Jacobi} {Equations} with the {Caputo} {Time-Fractional} {Derivative}},
     journal = {Minimax theory and its applications},
     year = {2020},
     volume = {5},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/MTA_2020_5_2_a2/}
}
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Fabio Camilli,Serikbolsyn Duisembay. Approximation of Hamilton-Jacobi Equations with the Caputo Time-Fractional Derivative. Minimax theory and its applications, Tome 5 (2020) no. 2. http://geodesic.mathdoc.fr/item/MTA_2020_5_2_a2/