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Showing 1 to 20 of 7968 for “"equation"”.
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Efficient high-order integral equation methods for the heat equation
Efficient high-order integral equation methods have been developed for solving the boundary value problems of the heat equation with complex geometries in two and three dimensions. First of all, the classical heat potential theory is applied to convert such problems to Volterra integral equations …
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On Gassmann's equation
Includes bibliographical references (pages 213-219).
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Separation of Laplace's equation
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1948.
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A Numerical Method for solving the Periodic Burgers' Equation through a Stochastic Differential Equation
The Burgers equation, and related partial differential equations (PDEs), can be numerically challenging for small values of the viscosity parameter. For example, these equations can develop discontinuous solutions (or solutions with large gradients) from smooth initial data. Aside from numerical …
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Modified Stochastic Sine-Gordon Equation
… is the Modified Stochastic Sine-Gordon Equation: utt = 2uxx − ut − sin(|u|^(&gamma)) + b(u, du/dt)dW/dt where &gamma > 0 is the parameter of the power of non-linearity, &delta &ge 0 is the magnitude of non-linearity, &alpha> 0 be the damping parameter, and &sigma the diffusion intensity, …
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Laplace's equation on perturbed domains
Laplace's equation is a prototypical elliptic PDE that appears in many electromagnetic and fluid dynamics problems. We develop two methods for solving Laplace's equation on domains that are perturbations of a circle. These methods are derived from governing equations and applied to several test …
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Schrödinger equation with periodic potentials.
The Schrödinger equation ... is considered. The solution of this equation is reduced to the problem of finding the eigenvectors of an infinite matrix. The infinite matrix is truncated to a finite matrix. The approximation due to the truncation is carefully studied. The band structure of the …
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On Initial-Boundary Value Problems for the Nonlinear Schroedinger Equation and the Ginzburg-Landau Equation
… of the forced nonlinear Schrodinger equation (NLS) is shown in Chapter 1. The global solution to an initial-boundary value problem for the NLS is proved in Chapter 2. Global existence of the full-line problem for the Ginzburg-Landau equation (GL) is shown in Chapter 3. In Chapter 4, …
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Evaluation of a Fractional Theis Equation
… local manner, a generalized groundwater flow equation was developed by Cloot and Botha (2006). This thesis analyzes the flow equation, based on non- integer order derivatives and its numerical implementation developed by Cloot and Botha. However, their equation was found faulty and a new …
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Pell's Equation and nearly equilateral triangles
… this family, we find an application of Pell's Equation. We follow this with a few other interesting notes on Pell's Equation.
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New Treatment Of The Pulsar Equation
In solving the pulsar equation, two methods have risen to the forefront, the CKF method (Contopoulos, Kazanas, and Fendt), and the TOTS method (Takamori, Okawa, Takamoto, and Suwa). Both methods are implemented by numerical relaxation, which creates problems at a singular surface known as the light …
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Dispersive Estimates for the Schrodinger Equation
… a problem involving the non-linear Schrodinger equation. In particular, we consider the following equation that arises in fiber optic communication systems, iut+dtu xx+u2u=0. We can reduce this to a non-linear, non-local eigenvalue equation that describes the so-called dispersion management …
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Dispersive estimates for the Schrödinger equation
Item withdrawn by Mark Zulauf (zulauf@illinois.edu) on 2010-06-30T12:54:50Z Item was in collections: University of Illinois Theses & Dissertations (ID: 1) No. of bitstreams: 1 Green_William.pdf: 999536 bytes, checksum: 87eb33f24c92fd62a4874b5db34bf8da (MD5)
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Reduced basis method for Boltzmann equation
… BGK model of the Knudsen parameterized Boltzmann equation which is 1-d with respect to both space and velocity. In order to solve the Boltzmann equation, we first transform the original differential equation by replacing the dependent variable with another variable, weighted with function t(y); …
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Integral equation theories for complex fluids
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Chemical Engineering, 1994.
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Analysis of the generalized Boltzmann equation.
Thesis: M.S., Massachusetts Institute of Technology, Department of Nuclear Engineering, 1972
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On initialization of primitive equation models
Thesis. 1975. M.S.--Massachusetts Institute of Technology. Dept. of Meteorology.
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The Fermat equation over quadratic fields
… conditions it is shown that the Fermat equation of exponent p has no solution over Q(√m) when p is a m-regular prime. Completely analogous to the work of Kummer, it is shown that m-regular primes can be described in terms of the generalized Bernoulli numbers. When p = 3,5 and 7, an …
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A control problem for Burgers' equation
Burgers' equation is a one-dimensional simple model for convection-diffusion phenomena such as shock waves, supersonic flow about airfoils, traffic flows, acoustic transmission, etc. For high Reynolds number, the open-loop system (no control) produces steep gradients due to the nonlinear nature of …
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