A discretization size and step size varying strategy in the numerical solution of I-Dimensional Schrodinger Equation

In this thesis we present a numerical solution of the I-dimensional Schrodinger equation using the method of lines approach (MOL) where we discretize the spatial dimension using some finite difference approximation leaving the time dimension to be the only independent variable in the resulting syste...

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Main Author:	Sa'adu, Lawal
Format:	Thesis
Language:	English
Subjects:	Schrodinger equation
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spelling	my-usim-ddms-122822024-05-29T20:07:27Z A discretization size and step size varying strategy in the numerical solution of I-Dimensional Schrodinger Equation Sa'adu, Lawal In this thesis we present a numerical solution of the I-dimensional Schrodinger equation using the method of lines approach (MOL) where we discretize the spatial dimension using some finite difference approximation leaving the time dimension to be the only independent variable in the resulting system of initial value problems. We study the effect of changing in the discretization size on the accuracy of the solution procedure versus changing the step size in the integration of the resulting differential equation. In the study we incorporate the use of Simpson's rule function in MATLAB. The results indicated that there are some advantages in deciding between the discretization sizes or step size in the numerical solution of differential equation as far as the computing time is concerned. Universiti Sains Islam Malaysia 2010 Thesis en https://oarep.usim.edu.my/handle/123456789/12282 https://oarep.usim.edu.my/bitstreams/ed64fc81-76db-457b-bc5d-c361868d2a0c/download 8a4605be74aa9ea9d79846c1fba20a33 https://oarep.usim.edu.my/bitstreams/f5b5ac75-20f4-4821-96e1-4001c6703e53/download 8d12b2e99e34233e9aab2fe215228287 https://oarep.usim.edu.my/bitstreams/c2ece34e-3fa0-4b03-8627-7353f50c92c2/download bb71ce2e3a395315905e21f141869aa6 https://oarep.usim.edu.my/bitstreams/49d31285-30a2-4032-a9ab-69815f5fd57d/download edf31467d35abc5d13ca10f6134b1d4b https://oarep.usim.edu.my/bitstreams/02308d37-7210-4510-a9e4-9307a1eb4009/download f92f8b4aa3d704357ca9238c5d97a667 https://oarep.usim.edu.my/bitstreams/3b0a1537-87cb-4bd3-87cd-deb96ecd851e/download a49f61304743375743e8b0173902e952 https://oarep.usim.edu.my/bitstreams/4ab1ff41-eefe-4cb1-9d7a-e7782f46afb8/download c272c6351b5d4d175839ceba49a84e3d https://oarep.usim.edu.my/bitstreams/2278f4be-954e-455a-b0a7-c5dc83954aad/download 0471be971dc5884419f44fee6067a9e6 https://oarep.usim.edu.my/bitstreams/e5b2fd83-2537-48ce-9a26-de4d53297cc7/download e13a1f2cdbdfdc183ffaa4531dd0c762 https://oarep.usim.edu.my/bitstreams/2867c423-6d57-4d11-9c3e-6a4cf6694554/download 68b329da9893e34099c7d8ad5cb9c940 https://oarep.usim.edu.my/bitstreams/48ab7f3e-9e9d-46ec-b8d0-adf768e34b11/download 61ac41675055b1b8ae283c5169fbec22 https://oarep.usim.edu.my/bitstreams/493441bc-c715-479a-9c1d-20d5ba6fab81/download 6d93d3216dc4a7f5df47d4876fbec4d3 https://oarep.usim.edu.my/bitstreams/49655a79-1c43-4acd-abef-aa13e2aa862d/download 70cf152f5dddabbf3e3e3a8bc23d0095 https://oarep.usim.edu.my/bitstreams/3190f4d7-75ed-4094-acfe-707c2f7c1e9f/download 48175cc56e52e020bf178616c0977374 https://oarep.usim.edu.my/bitstreams/4a6cb74e-a1bf-45ac-9f98-92b5179bf48a/download 884e307a96265ab0e1bf7bcc1f89c892 https://oarep.usim.edu.my/bitstreams/aac88887-9daf-46de-be86-17614f212b5f/download 2228e977ebea8966e27929f43e39cb67 https://oarep.usim.edu.my/bitstreams/520f08a0-e182-4063-977e-bc38477eeb21/download 1abb17524afa00a251ba82b97dccaf75 Schrodinger equation
institution	Universiti Sains Islam Malaysia
collection	USIM Institutional Repository
language	English
topic	Schrodinger equation
spellingShingle	Schrodinger equation Sa'adu, Lawal A discretization size and step size varying strategy in the numerical solution of I-Dimensional Schrodinger Equation
description	In this thesis we present a numerical solution of the I-dimensional Schrodinger equation using the method of lines approach (MOL) where we discretize the spatial dimension using some finite difference approximation leaving the time dimension to be the only independent variable in the resulting system of initial value problems. We study the effect of changing in the discretization size on the accuracy of the solution procedure versus changing the step size in the integration of the resulting differential equation. In the study we incorporate the use of Simpson's rule function in MATLAB. The results indicated that there are some advantages in deciding between the discretization sizes or step size in the numerical solution of differential equation as far as the computing time is concerned.
format	Thesis
author	Sa'adu, Lawal
author_facet	Sa'adu, Lawal
author_sort	Sa'adu, Lawal
title	A discretization size and step size varying strategy in the numerical solution of I-Dimensional Schrodinger Equation
title_short	A discretization size and step size varying strategy in the numerical solution of I-Dimensional Schrodinger Equation
title_full	A discretization size and step size varying strategy in the numerical solution of I-Dimensional Schrodinger Equation
title_fullStr	A discretization size and step size varying strategy in the numerical solution of I-Dimensional Schrodinger Equation
title_full_unstemmed	A discretization size and step size varying strategy in the numerical solution of I-Dimensional Schrodinger Equation
title_sort	discretization size and step size varying strategy in the numerical solution of i-dimensional schrodinger equation
granting_institution	Universiti Sains Islam Malaysia
url	https://oarep.usim.edu.my/bitstreams/f5b5ac75-20f4-4821-96e1-4001c6703e53/download https://oarep.usim.edu.my/bitstreams/c2ece34e-3fa0-4b03-8627-7353f50c92c2/download https://oarep.usim.edu.my/bitstreams/49d31285-30a2-4032-a9ab-69815f5fd57d/download https://oarep.usim.edu.my/bitstreams/02308d37-7210-4510-a9e4-9307a1eb4009/download https://oarep.usim.edu.my/bitstreams/3b0a1537-87cb-4bd3-87cd-deb96ecd851e/download https://oarep.usim.edu.my/bitstreams/4ab1ff41-eefe-4cb1-9d7a-e7782f46afb8/download https://oarep.usim.edu.my/bitstreams/2278f4be-954e-455a-b0a7-c5dc83954aad/download https://oarep.usim.edu.my/bitstreams/e5b2fd83-2537-48ce-9a26-de4d53297cc7/download
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A discretization size and step size varying strategy in the numerical solution of I-Dimensional Schrodinger Equation

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