TY - JOUR
T1 - Approximation of hamilton-jacobi equations with the caputo time-fractional derivative
AU - Camilli, Fabio
AU - Duisembay, Serikbolsyn
N1 - KAUST Repository Item: Exported on 2021-06-30
PY - 2020/1/1
Y1 - 2020/1/1
N2 - 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.
AB - 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.
UR - http://hdl.handle.net/10754/669817
UR - https://arxiv.org/pdf/1906.06868v1.pdf
UR - http://www.scopus.com/inward/record.url?scp=85108450537&partnerID=8YFLogxK
M3 - Article
SN - 2199-1421
VL - 5
SP - 199
EP - 220
JO - Minimax Theory and its Applications
JF - Minimax Theory and its Applications
IS - 2
ER -