Search for dissertations about: "thesis on differential equation"

Showing result 1 - 5 of 220 swedish dissertations containing the words thesis on differential equation.

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

   Author : Fredrik Lindgren; Göteborgs universitet; Göteborgs universitet; Gothenburg University; []
   Keywords : 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. Higher order differential operators on graphs

   Author : Jacob Muller; Pavel Kurasov; Ram Band; Stockholms universitet; []
   Keywords : NATURAL SCIENCES; NATURVETENSKAP; 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

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

   Author : Andreas Petersson; Chalmers University of Technology; []
   Keywords : 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

6. 4. 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

7. 5. On computational methods for nonlinear estimation

   Author : Thomas Schön; Linköpings universitet; []
   Keywords : ENGINEERING AND TECHNOLOGY; TEKNIK OCH TEKNOLOGIER; Nonlinear estimation; Particle filter; Kalman filter; System identification; Convex optimization; Differential-algebraic equation; TECHNOLOGY; TEKNIKVETENSKAP;

   Abstract : The Bayesian approach provides a rather powerful framework for handling nonlinear, as well as linear, estimation problems. We can in fact pose a general solution to the nonlinear estimation problem. However, in the general case there does not exist any closed-form solution and we are forced to use approximate techniques. READ MORE