Spelling suggestions: "subject:"differential equations, partial"" "subject:"ifferential equations, partial""
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On the application of partial differential equations and fractional partial differential equations to images and their methods of solutionJacobs, Byron 11 August 2014 (has links)
This body of work examines the plausibility of applying partial di erential equations and
time-fractional partial di erential equations to images. The standard di usion equation
is coupled with a nonlinear cubic source term of the Fitzhugh-Nagumo type to obtain a
model with di usive properties and a binarizing e ect due to the source term. We examine
the e ects of applying this model to a class of images known as document images;
images that largely comprise text. The e ects of this model result in a binarization process
that is competitive with the state-of-the-art techniques. Further to this application,
we provide a stability analysis of the method as well as high-performance implementation
on general purpose graphical processing units. The model is extended to include
time derivatives to a fractional order which a ords us another degree of control over this
process and the nature of the fractionality is discussed indicating the change in dynamics
brought about by this generalization. We apply a semi-discrete method derived by
hybridizing the Laplace transform and two discretization methods: nite-di erences and
Chebyshev collocation. These hybrid techniques are coupled with a quasi-linearization
process to allow for the application of the Laplace transform, a linear operator, to a
nonlinear equation of fractional order in the temporal domain. A thorough analysis
of these methods is provided giving rise to conditions for solvability. The merits and
demerits of the methods are discussed indicating the appropriateness of each method.
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Smoothness conditions and symmetries of partial differential equationsMamba, Siphamandla 10 May 2016 (has links)
A research report submitted to the Faculty of Science,
University of the Witwatersrand, in ful lment of the
requirements for the degree of Master of Science.
School of Mathematics
Johannesburg
February 15, 2016 / We obtain a solution of the Black-Scholes equation with a non-smooth bound-
ary condition using symmetry methods. The Black-Scholes equation along
with its boundary condition are rst transformed into the one dimensional
heat equation and an initial condition respectively. We then nd an appro-
priate general symmetry generator of the heat equation using symmetries of
the heat equation and the fundamental solution of the heat equation. The
method we use to nd the symmetry generator is such that the boundary
condition is left invariant and yet the symmetry can still be used to solve
the heat equation. We then use the help of Mathematica to nd the solution
to the heat equation. Then the solution is then transformed backwards to
a solution of the Black-Scholes equation using the same change of variables
that were used for the forward transformations. The solution is then nally
checked if it satis es the boundary condition of the Black-Scholes equation.
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Recent developments for numerical solutions of elliptic equations with random coefficients. / CUHK electronic theses & dissertations collectionJanuary 2013 (has links)
Zhou, Qianwen. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2013. / Includes bibliographical references (leaves 80-87). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstracts also in Chinese.
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Two modifications to the software interface package for nonlinear partial differential equationsMorse, Richard Lee January 2010 (has links)
Digitized by Kansas Correctional Industries
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Zur Theorie der gewöhnlichen Differentialgleichungen und der partiellen Differentialgleichungen zweiter Ordnung die Lösungen als Funktionen der Randwerte und der Parameter /Lichtenstein, Leon, January 1900 (has links)
Thesis (doctoral)--Friedrich-Wilhelms-Universität zu Berlin, 1909. / "Estratto dal tomo XXVIII (2 sem. 1909)del Rendiconti del Circolo matematico di Palermo"--P. 1. Vita.
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Jacobische Differentialgeometric und Systeme partieller Differentialgleichungen 1. OrdnungBreuer, Manfred. January 1958 (has links)
Inaug.-Diss.-Bonn.
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A condition concerning the existence of continuous solutions to Poisson's equationCook, Frederick Lee 12 1900 (has links)
No description available.
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Existence theorems for singular elliptic and parabolic partial differential equationsKrantzberg, Julius A. January 1969 (has links)
No description available.
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Pseudo-differential operators with rough coefficients /Wang, Luqi. January 1997 (has links)
Thesis ( Ph.D. ) -- McMaster University, 1997. / Includes bibliographical references (leaves 63-66). Also available via World Wide Web.
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Maximal estimates of solutions to dispersive partial differential equations.Wang, Sichun. Heinig, H.P. Unknown Date (has links)
Thesis (Ph.D.)--McMaster University (Canada), 1996. / Source: Dissertation Abstracts International, Volume: 57-10, Section: B, page: 6300. Adviser: H. P. Heinig.
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