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- Ljung, Lennart, 1946-, et al.
(författare)
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Adaptive System Performance in the Frequency Domain
- 1992
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Ingår i: Adaptive systems in control and signal processing 1992. - Linköping : Linköping University. - 9780080425962 ; , s. 33-40
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Konferensbidrag (refereegranskat)
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- Asadzadeh, Mohammad, 1952, et al.
(författare)
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The discrete ordinates method for the neutron transport equation in an infinite cylindrical domain
- 1992
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Ingår i: Mathematical Models and Methods in Applied Science. ; 2:3, s. 317-338
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Tidskriftsartikel (refereegranskat)abstract
- We prove a regularity result for a Fredholm integral equation with weakly singular kernel, arising in connection with the neutron transport equation in an infinite cylindrical domain. The theorem states that the solution has almost two derivatives in L1, and is proved using Besov space techniques. This result is applied in the error analysis of the discrete ordinates method for the numerical solution of the neutron transport equation. We derive an error estimate in the L1-norm for the scalar flux, and as a consequence, we obtain an error bound for the critical eigenvalue.
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- Ekolin, Gunnar, 1962
(författare)
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On Numerical Methods for the Diffusion Equation Subject to Non-Local Boundary Conditions
- 1992
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- 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. Results from a numerical experiment are presented. The second paper is devoted to Galerkin finite element methods for the general heat equation in one space dimension subject to specification of mass. The problem is rewritten as a system of two boundary value problems, of which the first is standard and the second involves the nonlocal specification of mass condition. A semidiscrete version, as well as time discretizations using the backward Euler and the Crank-Nicolson schemes, are studied for the second part of the system of boundary value problems. Error estimates showing rates of convergence are derived. Results from some numerical experiments are presented. In the third paper spatially interior error and stability estimates for approximations of derivatives of the solution to a parabolic problem are derived. These estimates are uniform down to t = 0. The spatially discrete equation and time discretizations using the backward Euler or a two level backward difference method are studied. These results are applied in the second paper above.
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