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Fast method of particular solutions ...

Lamichhane, Anup Raja.

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Fast method of particular solutions for solving partial differential equations.

Record Type:	Electronic resources : Monograph/item
Title/Author:	Fast method of particular solutions for solving partial differential equations./
Author:	Lamichhane, Anup Raja.
Published:	Ann Arbor : ProQuest Dissertations & Theses, : 2016,
Description:	99 p.
Notes:	Source: Dissertation Abstracts International, Volume: 78-05(E), Section: B.
Contained By:	Dissertation Abstracts International78-05B(E).
Subject:	Applied mathematics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10172977
ISBN:	9781369277654

Fast method of particular solutions for solving partial differential equations.
Lamichhane, Anup Raja.

Fast method of particular solutions for solving partial differential equations. - Ann Arbor : ProQuest Dissertations & Theses, 2016 - 99 p.

Source: Dissertation Abstracts International, Volume: 78-05(E), Section: B.

Thesis (Ph.D.)--The University of Southern Mississippi, 2016.

Method of particular solutions (MPS) has been implemented in many science and engineering problems but obtaining the closed-form particular solutions, the selection of the good shape parameter for various radial basis functions (RBFs) and simulation of the largescale problems are some of the challenges which need to be overcome. In this dissertation,we have used several techniques to overcome such challenges.

ISBN: 9781369277654Subjects--Topical Terms:

2122814
Applied mathematics.

Fast method of particular solutions for solving partial differential equations.
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100 1 $a Lamichhane, Anup Raja. $3 3283689
245 1 0 $a Fast method of particular solutions for solving partial differential equations.
260 1 $a Ann Arbor : $b ProQuest Dissertations & Theses, $c 2016
300 $a 99 p.
500 $a Source: Dissertation Abstracts International, Volume: 78-05(E), Section: B.
500 $a Adviser: Ching-Shyang Chen.
502 $a Thesis (Ph.D.)--The University of Southern Mississippi, 2016.
520 $a Method of particular solutions (MPS) has been implemented in many science and engineering problems but obtaining the closed-form particular solutions, the selection of the good shape parameter for various radial basis functions (RBFs) and simulation of the largescale problems are some of the challenges which need to be overcome. In this dissertation,we have used several techniques to overcome such challenges.
520 $a The closed-form particular solutions for the Matern and Gaussian RBFs were not known yet. With the help of the symbolic computational tools, we have derived the closed-form particular solutions of the Matern and Gaussian RBFs for the Laplace and biharmonic operators in 2D and 3D. These derived particular solutions play an important role in solving inhomogeneous problems using MPS and boundary methods such as boundary element methods or boundary meshless methods.
520 $a In this dissertation, to select the good shape parameter, various existing variable shape parameter strategies and some well-known global optimization algorithms have also been applied. These good shape parameters provide high accurate solutions in many RBFs collocation methods.
520 $a Fast method of particular solutions (FMPS) has been developed for the simulation of the large-scale problems. FMPS is based on the global version of the MPS. In this method, partial differential equations are discretized by the usual MPS and the determination of the unknown coefficients is accelerated using a fast technique. Numerical results confirm the efficiency of the proposed technique for the PDEs with a large number of computational points in both two and three dimensions. We have also solved the time fractional diffusion equations by using MPS and FMPS.
590 $a School code: 0211.
650 4 $a Applied mathematics. $3 2122814
650 4 $a Mathematics. $3 515831
690 $a 0364
690 $a 0405
710 2 $a The University of Southern Mississippi. $b Mathematics. $3 3280912
773 0 $t Dissertation Abstracts International $g 78-05B(E).
790 $a 0211
791 $a Ph.D.
792 $a 2016
793 $a English
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10172977