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1. 1. Contributions to Numerical Solution of Stochastic Differential Equations

   Författare :Anders Muszta; Göteborgs universitet; []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; adaptive method; change of time; CIR model; CKLS model; convergence order; Euler method; heavy-tailed SDE; hyperbolic SDE; geometric integration; global Lipschitz condition; Levy process; Lie group method; local Lipschitz condition; local martingales; mean reversion; Milstein method; numerical method; semimartingale; stochastic differential equation; stochastic Taylor expansion; strong approximation; symplectic integration; volatility induced stationarity; waveform relaxation; volatility induced stationarity;

   Sammanfattning : This thesis consists of four papers: Paper I is an overview of recent techniques in strong numerical solutions of stochastic differential equations, driven by Wiener processes, that have appeared the last then 10 years, or so. Paper II studies theoretical and numerical aspects of stochastic differential equations with so called volatility induced stationarity. LÄS MER

3. 2. Group theoretical methods for solving multidimensional nonlinear partial differential equations

   Författare :Marianna Euler; Luleå tekniska universitet; []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Mathematics; Matematik;

   Sammanfattning : New methods for constructing both exact and approximate solutions of multidimensional nonlinear partial differential equations are developed. The basis of the methods is taken from the classical Lie transformation group theory. LÄS MER

4. 3. Efficient Solvers for Space-Time Discontinuous Galerkin Spectral Element Methods

   Författare :Lea Miko Versbach; Numerisk analys; []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; NATURVETENSKAP; NATURAL SCIENCES; Discontinuous Galerkin Method; Spectral Element Method; Finite Volume Method; Implicit Schemes; Preconditioner; Multigrid Method; Space-Time; Lobatto IIIC Method; Local Fourier Analysis;

   Sammanfattning : In this thesis we study efficient solvers for space-time discontinuous Galerkin spectral element methods (DG-SEM). These discretizations result in fully implicit schemes of variable order in both spatial and temporal directions. LÄS MER

5. 4. On Numerical Methods for the Diffusion Equation Subject to Non-Local Boundary Conditions

   Författare :Gunnar Ekolin; Göteborgs universitet; []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; forward Euler method; backward Euler method; the Crank-Nicolson method; heat equation; Galerkin finite element methods; backward Euler method;

   Sammanfattning : In the first paper three different finite difference methods for solving the heat equation in one space dimension with boundary conditions containing integrals over the interior of the interval are considered. The schemes are based on the forward Euler, the backward Euler and the Crank-Nicolson methods. Error estimates are derived in maximum norm. LÄS MER

7. 5. Efficiency factors for space heating system in buildings

   Författare :Christian Brembilla; Thomas Olofsson; Ronny Östin; Mohsen Soleimani-Mohseni; Bjørn Reidar Sørensen; Umeå universitet; []
   Nyckelord :TEKNIK OCH TEKNOLOGIER; ENGINEERING AND TECHNOLOGY; Efficiency factors of space heating; hydronic panel radiator; hydronic floor heating; multilayer wall; numerical modelling; room control volume; decrement factor; time delay; heat conduction; heat convection; heat radiation; heat storage; thermal inertia; Euler solver; Newton-Raphson method; synthetic weather file; feedback and feed-forward control strategies; adaptive control; validation methodology; uncertainty bands; robustness of model predictions; thermostatic booth simulator; differential sensitivity analysis; transient model of panel radiator with multiple storage elements; active thermal mass; benchmark performance indicator; linear regression model; calibration through uncertainty bands; hybrid model of low-energy building: law driven data driven; outdoor temperature compensation heating curve; solar radiation model; finite difference method; heat equation;

   Sammanfattning : The thesis focuses on the efficiency of the space heating system. In particular, the efficiency factors measure the efficiency of thermal zone. The efficiency factors measures how the energy is used in a space heating. LÄS MER