78,383 research outputs found
Numerical Methods for Solving Fractional Differential Equations
Department of Mathematical SciencesIn this thesis, several efficient numerical methods are proposed to solve initial value problems and boundary value problems of fractional di???erential equations.
For fractional initial value problems, we propose a new type of the predictorevaluate-corrector-evaluate method based on the Caputo fractional derivative operator.
Furthermore, we propose a new type of the Caputo fractional derivative operator that does not have a di???erential form of a solution. However, with some fractional orders, there are problems that a solution blows up and the scheme has a low convergence. Thus, we identify new treatments for these values. Then, we can expect a significant improvement for all fractional orders. The advantages and improvements are shown by testing various numerical examples.
For fractional BVPs, we propose an explicit method that dramatically reduces the computational time for solving a dense matrix system. Moreover, by adopting
high-order predictor-corrector methods which have uniform convergence rates O(h2) or O(h3) for all fractional orders [8], we propose a second-order method and a third-order method by using the Newton???s method and the Halley method, respectively. We show its advantage by testing various numerical examples.clos
Some characterizations of spheres and elliptic paraboloids II
We show some characterizations of hyperspheres in the -dimensional
Euclidean space with intrinsic and extrinsic properties such
as the -dimensional area of the sections cut off by hyperplanes, the
-dimensional volume of regions between parallel hyperplanes, and the
-dimensional surface area of regions between parallel hyperplanes. We also
establish two characterizations of elliptic paraboloids in the
-dimensional Euclidean space with the -dimensional
area of the sections cut off by hyperplanes and the -dimensional volume
of regions between parallel hyperplanes. For further study, we suggest a few
open problems.Comment: 10 page
Photoproduction with Nucleon Resonances
We investigate the reaction mechanism of photoproduction off
the neutron target, i.e., , in the range of GeV. We employ an effective Lagrangian method at the tree-level Born
approximation combining with a Regge approach. As a background, the
-Reggeon trajectory is taken into account in the channel and
and hyperons in the -channel Feynman diagram. In addition, the role
of various nucleon resonances listed in the Particle Data Group (PDG) is
carefully scrutinized in the channel where the resonance parameters are
extracted from the experimental data and constituent quark model. We present
our numerical results of the total and differential cross sections and compare
them with the recent CLAS data. The effect of the narrow nucleon resonance
on cross sections is studied in detail and it turns out that
its existence is essential in photoproduction to reproduce the
CLAS data.Comment: 4 pages, 3 figures, Proceedings of "8th International Conference on
Quarks and Nuclear Physics (QNP2018)", November 13-17, 2018, Tsukuba, Japa
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