A Schwarz waveform relaxation method for time-dependent space fractional Schrödinger/heat equations

Xavier Antoine (1, 2) , Emmanuel Lorin (3, 4)

1 SPHINX - Systems with physical heterogeneities : inverse problems, numerical simulation, control and stabilization
2 EDP - Equations aux dérivées partielles
3 CRM - Centre de Recherches Mathématiques [Montréal]
4 Carleton University

This paper is dedicated to the derivation and analysis of a Schwarz waveform relaxation domain decomposition method for solving time-dependent linear/nonlinear space fractional Schrödinger and heat equations. Along with the details of the derivation of the method and some mathematical properties, we also propose some illustrating numerical experiments and conjectures on the rate of convergence of the method.

Mots clés: space fractional Schrödinger equation; space fractional heat equation; fractional Laplacian; domain decomposition method; Schwarz relaxation waveform algorithm

Domaines: Equations aux dérivées partielles [math.AP]; Analyse numérique [math.NA]

Xavier Antoine, Emmanuel Lorin. A Schwarz waveform relaxation method for time-dependent space fractional Schrödinger/heat equations. Applied Numerical Mathematics, 2022, 182, pp.248-264. ⟨10.1016/j.apnum.2022.07.012⟩. ⟨hal-03119456⟩