Search for dissertations about: "thesis on differential equation"
Showing result 1 - 5 of 220 swedish dissertations containing the words thesis on differential equation.
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1. On weak and strong convergence of numerical approximations of stochastic partial differential equations
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
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2. Higher order differential operators on graphs
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
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3. Approximating Stochastic Partial Differential Equations with Finite Elements: Computation and Analysis
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
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4. A Study of Smooth Functions and Differential Equations on Fractals
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
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5. On computational methods for nonlinear estimation
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
