Strong Rates of Convergence of a Splitting Scheme for Schrödinger Equations with Nonlocal Interaction Cubic Nonlinearity and White Noise Dispersion

• We analyze a splitting integrator for the time discretization of the Schrodinger equation with nonlocal interaction cubic nonlinearity and white noise dispersion. We prove that this time integrator has order of convergence one in the pth mean sense, for any p > 1 in some Sobolev spaces. We prove that the splitting schemes preserves the L2-norm, which is a crucial property for the proof of the strong convergence result. Finally, numerical experiments illustrate the performance of the proposed numerical scheme.

Subject headings

NATURVETENSKAP  -- Matematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics (hsv//eng)

NATURVETENSKAP  -- Matematik -- Beräkningsmatematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Computational Mathematics (hsv//eng)

TEKNIK OCH TEKNOLOGIER  -- Elektroteknik och elektronik -- Reglerteknik (hsv//swe)

ENGINEERING AND TECHNOLOGY  -- Electrical Engineering, Electronic Engineering, Information Engineering -- Control Engineering (hsv//eng)

NATURVETENSKAP  -- Matematik -- Matematisk analys (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Mathematical Analysis (hsv//eng)

Keyword

nonlocal interaction cubic nonlinearity

splitting integrators

stochastic Schródinger equations

strong convergence rates

white noise dispersion

Association reactions

Control nonlinearities

Dispersions

Sobolev spaces

White noise

Convergence rates

Cubic nonlinearities

Noise dispersion

Non-local interactions

Splitting integrator

Splittings

Stochastic schródinge equation

Stochastics

Strong convergence

Strong convergence rate

Stochastic systems

strong convergence rates

Publication and Content Type

ref (subject category)

art (subject category)