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Visar resultat 1 - 5 av 57 avhandlingar som matchar ovanstående sökkriterier.
1. Group theoretical methods for solving multidimensional nonlinear partial differential equations
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
2. On Numerical Methods for the Diffusion Equation Subject to Non-Local Boundary Conditions
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
3. Computer-Assisted Proofs and Other Methods for Problems Regarding Nonlinear Differential Equations
Sammanfattning : This PhD thesis treats some problems concerning nonlinear differential equations. In the first two papers computer-assisted proofs are used. The differential equations there are rewritten as fixed point problems, and the existence of solutions are proved. LÄS MER
4. Finite element approximation of the linear stochastic Cahn-Hilliard equation
Sammanfattning : The linearized Cahn-Hilliard-Cook equation is discretized in the spatial variables by a standard finite element method. Strong convergence estimates are proved under suitable assumptions on the covariance operator of the Wiener process, which is driving the equation. The backward Euler time stepping is also studied. LÄS MER
5. Data Assimilation in Fluid Dynamics using Adjoint Optimization
Sammanfattning : Data assimilation arises in a vast array of different topics: traditionally in meteorological and oceanographic modelling, wind tunnel or water tunnel experiments and recently from biomedical engineering. Data assimilation is a process for combine measured or observed data with a mathematical model, to obtain estimates of the expected data. LÄS MER