Home > New B-Spline Approximations for Numerical Solution of Initial and Boundary Value Problems
Thesis Info
Access Option
Author
Iqbal, Muhammad Kashif
Program
PhD
Institute
National College of Business Administration and Economics
City
Lahore
Province
Punjab
Country
Pakistan
Thesis Completing Year
2019
Thesis Completion Status
Completed
Subject
Physical Sciences
Language
English
Link
http://prr.hec.gov.pk/jspui/bitstream/123456789/10886/1/Muhammad%20Kashif%20Iqbal_Computational%20Maths_2019_NCBAE_PRR.pdf
Added
2021-02-17 19:49:13
Modified
2024-03-24 20:25:49
ARI ID
1676724883290
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In this work, new cubic, quartic and quintic B-spline approximations are proposed for approximate solution of initial and boundary value problems. The error analysis of these new approximations has been executed, which affirms their uniform convergence in entire spatial domain. The numerical algorithms based on B-spline functions assembled with new approximations are developed for numerical solution of second, third and fourth singular initial and boundary value problems. The L''Hospital''s Rule has been utilized for removal of singularities. The non-linear equation is first changed into a system of linear equations with the help of quasi-linearization technique and then solved by a modified form of well known Thomas algorithm. Moreover, numerical schemes based on usual finite difference formulation and new B-spline approximations are also presented for numerical solution of three non-linear mathematical models named as Klein-Gordon equation, Korteweg-de Vries equation and Kuramoto-Sivashinsky equation. The finite difference formulation is used for temporal discretization, whereas, new B--spline approximations based on Crank--Nicolson scheme have been used to interpolate the solution in space direction. The proposed numerical schemes are proved to be unconditionally stable subject to the Von-Neuman stability analysis. In order to corroborate this work, several test examples have been considered and the computational outcomes are compared with existing numerical techniques. It is revealed that by virtu of simple and straightforward implementation, our new B-spline approximations produce more accurate outcomes as compared to other variants on the topic.
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37. Al-Saffat/The Rows
37. Al-Saffat/The Rows
I/We begin by the Blessed Name of Allah
The Immensely Merciful to all, The Infinitely Compassionate to everyone.
37:01
a. By those lining up in rows,
37:02
a. and those drivers, driving away,
37:03
a. and those reciting the Reminder – The Divine Qur’an.
37:04
a. Indeed, your Allah is the One and Only Allah of everyone.
b. HE has no parents, no partners, no siblings, no sons, and no daughters.
37:05
a. Allah is Rabb - The Lord of the celestial realm and the terrestrial world and whatever is
within and between them, and,
b. Allah is also Rabb - The Lord of the vast expanse of the East and the West.
37:06
a. Indeed, WE adorned the sky of the terrestrial world with splendor of the glittering stars.
37:07
a. And secured them with meteors against every defiant Satan.
37:08
a. So that they, who seek to know the unknowable, may not be able to eavesdrop on the Exalted Assembly of angels,
b. for they will be pelted with meteors from every side -
37:09
a. – and driven off,
b. for them will be a constant and perpetual punishment.
37:10
a. Except for the one, who is able to eavesdrop and snatch a word of such knowledge,
b. he is instantaneously pursued by flaming fireballs.
37:11
a. So ask them:
b. ‘Are they more difficult to be created, or those WE created others than them?
c. In fact, WE created them – the human species - out of mere sticky clay!