Sökning: "partial differential equation"

Visar resultat 1 - 5 av 139 avhandlingar innehållade orden partial differential equation.

1. 1. Numerical analysis and simulation of stochastic partial differential equations with white noise dispersion

   Författare :André Berg; David Cohen; Per Åhag; Guillaume Dujardin; Ludovic Goudenège; Umeå universitet; []
   Nyckelord :NATURAL SCIENCES; NATURVETENSKAP; NATURVETENSKAP; NATURAL SCIENCES; stochastic partial differential equation; mathematics; numerical analysis; numerical scheme; time integrator; convergence analysis; blowup; critical exponent; nonlinear Schrödinger equation; Manakov equation; Benjamin-Bona-Mahony equation; BBM equation; stochastic; random; dispersion; white noise dispersion; finite difference; pseudospectral; code; matlab; exponential integrator; splitting integrator; convergence in probability; Mathematics; matematik; Numerical Analysis; numerisk analys;

   Sammanfattning : This doctoral thesis provides a comprehensive numerical analysis and exploration of several stochastic partial differential equations (SPDEs). More specifically, this thesis investigates time integrators for SPDEs with white noise dispersion. LÄS MER

3. 2. On weak and strong convergence of numerical approximations of stochastic partial differential equations

   Författare :Fredrik Lindgren; Göteborgs universitet; Göteborgs universitet; Gothenburg University; []
   Nyckelord :Additive noise; Cahn-Hilliard-Cook equation; Error estimate; Finite element; Hyperbolic equation; Parabolic equation; Rational approximation; Stochastic partial differential equation; Strong convergence; Truncation; Wiener process; Weak convergence; Weak convergence;

   Sammanfattning : This thesis is concerned with numerical approximation of linear stochastic partial differential equations driven by additive noise. In the first part, we develop a framework for the analysis of weak convergence and within this framework we analyze the stochastic heat equation, the stochastic wave equation, and the linearized stochastic Cahn-Hilliard, or the linearized Cahn-Hilliard-Cook equation. LÄS MER

4. 3. Approximating Stochastic Partial Differential Equations with Finite Elements: Computation and Analysis

   Författare :Andreas Petersson; Chalmers University of Technology; []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Lévy process; Lyapunov equation; white noise; finite element method; multilevel Monte Carlo; Monte Carlo; multiplicative noise; asymptotic mean square stability; stochastic heat equation; covariance operator; weak convergence; generalized Wiener process; numerical approximation; stochastic wave equation; Stochastic partial differential equations;

   Sammanfattning : Stochastic partial differential equations (SPDE) must be approximated in space and time to allow for the simulation of their solutions. In this thesis fully discrete approximations of such equations are considered, with an emphasis on finite element methods combined with rational semigroup approximations. LÄS MER

5. 4. On the discretization in time and space of parabolic integro-differential equations

   Författare :Nai-Ying Zhang; Göteborgs universitet; Göteborgs universitet; Gothenburg University; []
   Nyckelord :initial-boundary value problem; parabolic; partial; integro-differential equation; regularity; nonsmooth initial data; finite element method; fully discrete; Galerkin approximation; stability; error estimate; quadrature; stability;

   Sammanfattning : .... LÄS MER

7. 5. Exponential integrators for stochastic partial differential equations

   Författare :Rikard Anton; David Cohen; Christian Engström; Stig Larsson; Annika Lang; Umeå universitet; []
   Nyckelord :NATURAL SCIENCES; NATURVETENSKAP; Stochastic partial differential equations; numerical methods; stochastic exponential integrator; strong convergence; trace formulas;

   Sammanfattning : Stochastic partial differential equations (SPDEs) have during the past decades become an important tool for modeling systems which are influenced by randomness. Because of the complex nature of SPDEs, knowledge of efficient numerical methods with good convergence and geometric properties is of considerable importance. LÄS MER