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Showing result 1 - 5 of 232 swedish dissertations matching the above criteria.

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

   Author : Fredrik Lindgren; Göteborgs universitet; []
   Keywords : NATURVETENSKAP; NATURAL SCIENCES; NATURVETENSKAP; NATURAL SCIENCES; 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;

   Abstract : 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. READ MORE

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

   Author : André Berg; David Cohen; Per Åhag; Guillaume Dujardin; Ludovic Goudenège; Umeå universitet; []
   Keywords : 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;

   Abstract : 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. READ MORE

5. 3. Higher order differential operators on graphs

   Author : Jacob Muller; Pavel Kurasov; Ram Band; Stockholms universitet; []
   Keywords : NATURVETENSKAP; NATURAL SCIENCES; Almost periodic functions; differential operators on metric graphs; quantum graphs; estimation of eigenvalues;

   Abstract : This thesis consists of two papers, enumerated by Roman numerals. The main focus is on the spectral theory of -Laplacians. Here, an -Laplacian, for integer , refers to a metric graph equipped with a differential operator whose differential expression is the -th derivative. READ MORE

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

   Author : Andreas Petersson; Chalmers tekniska högskola; []
   Keywords : NATURVETENSKAP; NATURAL SCIENCES; NATURVETENSKAP; NATURAL SCIENCES; 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;

   Abstract : 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. READ MORE

7. 5. A Study of Smooth Functions and Differential Equations on Fractals

   Author : Anders Pelander; Anders Öberg; Svante Janson; Alexander Teplyaev; Tom Lindström; Uppsala universitet; []
   Keywords : Mathematical analysis; Analysis on fractals; p.c.f. fractals; Sierpinski gasket; Laplacian; differential equations on fractals; infinite dimensional i.f.s.; invariant measure; harmonic functions; smooth functions; derivatives; products of random matrices; Matematisk analys;

   Abstract : In 1989 Jun Kigami made an analytic construction of a Laplacian on the Sierpiński gasket, a construction that he extended to post critically finite fractals. Since then, this field has evolved into a proper theory of analysis on fractals. The new results obtained in this thesis are all in the setting of Kigami's theory. READ MORE