In this paper, 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.
Approximation of Hamilton-Jacobi equations with Caputo time-fractional derivative
Fabio Camilli;
2020-01-01
Abstract
In this paper, 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.File in questo prodotto:
Non ci sono file associati a questo prodotto.
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
