Approximation of Hamilton-Jacobi equations with Caputo time-fractional derivative
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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 CFL condition and converges to the unique viscosity solution of the Hamilton-Jacobi equation.
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