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Ordinary differential equation methods for some optimization problemsZhang, Quanju 01 January 2006 (has links)
No description available.
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On the implementation of multigrid methods for the numerical solution of partial differential equationsDelaney, Allen Daniel January 1984 (has links)
A number of experimental implementations of the multigrid algorithm for the solution of systems of partial differential equations have been produced. One program is applicable to simple nonlinear
scalar equations, the others to linear equations, scalar and systems, which may be mildly stiff. All use nested grids and residual extrapolation techniques to compute solution and error estimates very economically. One version implements list based adaptive grids to further decrease both computation and storage needed for comparable problems. Each experiment was demonstrated
using a set of problems with known solutions
and the program performance or nonperformance
discussed. Several techniques were examined to ensure that the system of difference equations representing a given problem would be convergent. The use of artificial viscosity was found to be practical in the general case, though for linear problems the use of one-sided differencing may be superior. / Science, Faculty of / Computer Science, Department of / Graduate
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A symmetry analysis of a second order nonlinear diffusion equationJoubert, Ernst Johannes 03 April 2014 (has links)
M.Sc. (Mathematics) / Please refer to full text to view abstract
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Some Diophantine EquationsPressly, Kirby Smith 01 1900 (has links)
This paper will be devoted to an examination of several general and specific equations and systems of equations of the diophantine type. Only algebraic equations with integral coefficients, not all zero, will considered. The elementary properties of the integers will be assumed.
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Symmetry structures and conserved forms of systems of pdesAlqurashi, Bader Mutair January 2019 (has links)
A thesis submitted in fulfillment of the requirements for the degree of Doctor of Philosophy to the Faculty of Science, University of the Witwatersrand, Johannesburg, 2019 / We will study the symmetry, invariance properties and conservation laws of partial dif
ferential equations (pdes) that arise in a number of situations in mathematical physics.
These will be range from Image Processing and noise removal algorithms to Timoshenko
beam systems. Furthermore, we will study the invariance properties and approximate
conservation laws of some nonlinear Schro¨dinger equation with PT-symmetric potentials
with inhomogeneous nonlinearity and some nonlinear Schro¨dinger equation involving a
spatially extended system consisting of two coupled elements. / TL (2019)
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Domain decomposition algorithms for transport and wave propagation equationsGerardo Giorda, Luca 09 December 2002 (has links)
Not available
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On Integral Equations of the First Kind and Various Methods of Solution / Integral Equations of the First KindJansen, Siegfried 10 1900 (has links)
This thesis gives an account of most known methods which can be utilized to solve various integral equations of the first kind. / Thesis / Master of Science (MS)
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A Generalization of Newton's MethodLeBouf, Billy Ruth 08 1900 (has links)
It is our purpose here to investigate the method of solving equations for real roots by Newton's Method and to indicate a generalization arising from this method.
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Symmetry reductions, exact solutions and conservation laws of a variable coefficient (2+1)-dimensional zakharov-kuznetsov equation / Letlhogonolo Daddy Moleleki.Moleleki, Letlhogonolo Daddy January 2011 (has links)
This research studies two nonlinear problems arising in mathematical physics. Firstly
the Korteweg-de Vrics-Burgers equation is considered. Lie symmetry method is
used to obtain t he exact solutions of Korteweg-de Vries-Burgers equation. Also
conservation laws are obtained for this equation using the new conservation theorem.
Secondly, we consider the generalized (2+ 1)-dimensional Zakharov-Kuznctsov (ZK)
equation of time dependent variable coefficients from the Lie group-theoretic point
of view. We classify the Lie point symmetry generators to obtain the optimal system
of one-dimensional subalgebras of t he Lie symmetry algebras. These subalgebras arc
then used to construct a number of symmetry reductions and exact group-invariant
solutions of the ZK equation. We utilize the new conservation theorem to construct
the conservation laws of t he ZK equation. / Thesis (M. Sci in Applied Mathematics) North-West University, Mafikeng Campus, 2011
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Lie group analysis of certain nonlinear differential equations arising in fluid mechanics / Belinda Thembisa MatebeseMatebese, Belinda Thembisa January 2010 (has links)
This research studies two nonlinear differential equations arising in fluid mechanics.
Firstly, the Zakharov-Kuznetsov's equation in (3+1) dimensions with an arbitrary
power law nonlinearity is considered. The method of Lie symmetry analysis is used
to carry out the integration of Zakharov-Kuznetsov's equation. Also, the extended
tanh-function method and t he G'/G method are used to integrate the Zakharov-Kuznetsov's equation. The non-topological soliton solution is obtained by the aid of
solitary wave ansatz method. Numerical simulation is given to support the analytical
development.
Secondly. the nonlinear flow problem of an incompressible viscous fluid is considered.
The fluid is taken in a channel having two weakly permeable moving porous walls.
An incompressible fluid fills the porous space inside the channel. The fluid is magnetohydrodynamic
in the presence of a time-dependent magnetic field. Lie group
method is applied along with perturbation method in the derivation of analytic solution.
The effects of the magnetic field, porous medium, permeation Reynolds number
and wall dilation rate on the axial velocity arc shown and discussed. / Thesis (M.Sc.(Applied Mathematics) North-West University, Mafikeng Campus, 2010
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