Numerical approximation and simulation of the stochastic wave equation on the sphere

• Solutions to the stochastic wave equation on the unit sphere are approximated by spectral methods. Strong, weak, and almost sure convergence rates for the proposed numerical schemes are provided and shown to depend only on the smoothness of the driving noise and the initial conditions. Numerical experiments confirm the theoretical rates. The developed numerical method is extended to stochastic wave equations on higher-dimensional spheres and to the free stochastic Schrodinger equation on the unit sphere.

Ämnesord

NATURVETENSKAP  -- Matematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics (hsv//eng)

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

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

TEKNIK OCH TEKNOLOGIER  -- Maskinteknik -- Strömningsmekanik och akustik (hsv//swe)

ENGINEERING AND TECHNOLOGY  -- Mechanical Engineering -- Fluid Mechanics and Acoustics (hsv//eng)

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

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

Nyckelord

Gaussian random fields

Karhunen-Loeve expansion

Spherical harmonic

functions

Stochastic partial differential equations

Stochastic wave

equation

Stochastic Schrodinger equation

Sphere

Spectral Galerkin

methods

Strong and weak convergence rates

Almost sure convergence

gaussian random-fields

weak approximation

discretization

regularity

Mathematics

Gaussian random fields

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