Analysis of a Relaxation Scheme for a Nonlinear Schrödinger Equation Occurring in Plasma Physics

Abstract

This paper is devoted to the analysis of a relaxation-type numerical scheme for a nonlinear Schrödinger equation arising in plasma physics. The scheme is shown to be preservative in the sense that it preserves mass and energy. We prove the well-posedness of the semidiscretized system and prove convergence to the solution of the time-continuous model.

Keywords:

• relaxation scheme
• initial value problem
• Laplace equation
• nonlinear Schrödinger equation

AMS Subject Classification:

• 65M12
• 35Q40