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Spline Solutions for Some Fractional Order Boundary Value Problems

Thesis Info

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Author

Khalid, Nauman

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

Mathemaics

Language

English

Link

http://prr.hec.gov.pk/jspui/bitstream/123456789/14331/1/Nauman%20Khalid%20maths%202019%20ncbae%20lhr%20prr..pdf

Added

2021-02-17 19:49:13

Modified

2024-03-24 20:25:49

ARI ID

1676727227067

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In this thesis, the spline solutions to some fractional order boundary value problems have been proposed using different spline collocation techniques. The Caputo’s definition for fractional order derivatives is used, as it allows imposing the boundary constraint(s) in terms of integer order derivative(s). An efficient technique based on non-polynomial quintic spline functions, comprised of a trigonometric part and polynomial part, has been developed for solving fourth order fractional boundary value problems involving product terms. The C¥ differentiability of the trigonometric part of non-polynomial spline compensates for the loss of smoothness inherent in polynomial spline. The second and fourth order convergence of the presented algorithm has been discussed in detail. Moreover, the approximate solutions of three very important time fractional models, advection-diffusion equation, Allen-Cahn equation and diffusion-wave equation, have been studied by means of redefined and modified forms of cubic B-spline functions. The Caputo time-fractional derivatives have been discretized by finite difference formulations whereas B-spline functions are used for spatial discretization. The unconditional stability and theoretical convergence of proposed numerical algorithms have been proved rigorously. Some test examples have been considered for numerical experiments. The computational results are in line with theoretical expectations and exhibit a superior agreement with the analytical exact solutions as compared to the existing techniques.
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سلطان کھاروی دی حیاتی

سلطان کھاروی دی حیاتی

جنم

سلطان کھار وی 1965ء نوں پنڈ کھارا ضلع گوجرانوالاوچ پیدا ہوئے ۔

خاندانی پچھوکڑ

ساڈا پیارا دیس جیہدا ناں چوہدری رحمت علی نے رکھیا جیہدا سفنا علامہ اقبال نے ویکھیا تے جینہوں وجود وچ لیائون لئی قائد اعظم محمد علی جناح نے اپنیاں نیندراں دی قربانی دتی ۔ پاکستان تے بن گیا پر ظلم ایہہ ہویا جے پنجاب وچ لکیر مار دتی گئی ۔پنجاب د و ٹوٹے ہو گیا۔اک مشرقی تے اک مغربی پنجاب، جیہدے وچ اسیں تسیں رہندے آں ۔مشرقی پنجاب دے  مشہو ر ضلعے جالندھردے پنڈ تلوں دے نیڑے تیڑے ایہہ پنڈ اج وی موجود اے ۔ اوس پنڈ دا ناں اے کوٹ بادل خاں ۔بادل خاں کوئی سر کڈھ پٹھان سی جیہدی قبر اج وی کوٹ بادل خاں وچ موجود اے ۔ایس کوٹ بادل خاں توں 1947ء دی ونڈ مگروں اک خاندان ہجرت کر کے پاکستا ن آ یا ۔خاندان دے وڈے داناں سی (چوہدری بوڑا)جیہڑے سلطان کھاروی دے دادا سن ۔ چوہدری بوڑا 1958ء وچ فوت ہو ئے ۔اوہناں نوں کھارے دا نمبر دار بنا دتا گیا سی ۔ اوس سمے جدوں لوکائی اپنے اپنے ساکاں انگاں دی تلاش وچ ایدھر اودھر بھٹکدی پھر دی سی ۔

سلطان کھار وی دا پنڈ کھارا

ضلع شیخوپورہ دے مشہور پنڈ جنڈیا لا شیر خاں توں شمال نوں جائیے تے باراں تیراں کلومیٹر تے اک پنڈ اے ۔جدوں پاکستان بنیا تے ایس پنڈ وچ کوئی سو گھر وی نئیں سی ۔ایس پنڈ دا ناں اے ’’کھارا ‘‘ایہہ پنڈ ضلع گوجرانوالادی حدود وچ اے تے پنڈ کھارا وچ لنگھن والی سڑک سدھی گوجرنوالا دے اعوان چوک نال جا لگدی اے ۔

 

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