عنوان

Numerical Methods For Solving Riesz Space Fractional Partial Differential Equations Based On Polynomial Interpolants

Number

T27673

.Language of Text, Soundtrack etc

انگلیسی

Title Proper

Numerical Methods For Solving Riesz Space Fractional Partial Differential Equations Based On Polynomial Interpolants

General Material Designation

Dissertation

First Statement of Responsibility

Ihsan Lateef Saeed

Name of Publisher, Distributor, etc.

Mathematical Sciences

Date of Publication, Distribution, etc.

1401

Specific Material Designation and Extent of Item

122p.

Other Physical Details

cd

Dissertation or thesis details and type of degree

Ph.D.

Discipline of degree

Applied Mathematics

Date of degree

1401/08/10

Text of Note

In recent years, fractional calculus has been studied by many mathematicians andscientists. Scientists in the last decade found the fractional calculus useful in variousfields of science and engineering including fluid flow, biology, rheology, diffusivetransport, electrical networks, electromagnetic theory, probability potential theory,linear viscoelasticity, signal processing, control of engineering systems, viscoelasticpolymers, electrical circuits with reactance, electrochemistry, tracer fluid flows andelasticity. Fractional differential equations (FDEs) have important applications in manyareas like in the fields of viscoelastic materials, control theory, anomalous diffusion,signal processing, image filtering, electrochemical processes, fractal phenomena,polymer rheology, regular variation in thermodynamics, biophysics, blood flowphenomena, aerodynamics, electrodynamics of complex medium, viscoelasticity,bode analysis of feedback amplifiers, capacitor theory, electrical circuits, electroanalyticalchemistry, biology, control theory, fitting of experimental data.In most cases, fractional differential equations (FDEs) cannot be solved exactly,as a consequence, approximate and numerical techniques are playing an importantrole in identifying the solution behavior of such fractional equations and exploring theirapplications. The main objective of this thesis is to design new effective numericalmethods and supporting analysis, based on the finite difference method and splineinterpolation methods. In the second chapter, we design a new numerical method forthe Riesz space partial fractional differential equation that is a special case of thefractional kinetics equation. We utilize the piecewise linear interpolation polynomial toapproximate the Riesz fractional derivative. Next, we proposed, two numericalmethods based on the forward Euler and Crank-Nicolson methods for time, also linearinterpolation polynomial for space. Also, stability and convergence are proved. In thethird chapter, we consider the numerical solution of the Riesz space fractionaladvection-dispersion equation. First, the Riesz fractional derivative is approximatedwith respect to the space variable by using spline interpolation. Furthermore, we usethe Euler and the Crank-Nicolson schemes to approximate the time ordinaryderivative and get two different schemes. Second, using the matrix analysis method,we prove that the two difference schemes are unconditionally stable. Finally, somenumerical results are given, which demonstrate the effectiveness of the two differenceschemes.

Text of Note

معادلات دیفرانسیل کسری کاربردهای بسیاری در تمامی علوم از جمله پردازش تصویر، پردازش نویز، تئوریکنترل، بیو فیزیک، ترمودینامیک، پلیمر و غیره دارد. از آنجایی که حل تحلیلی معادلات دیفرانسیل کسریبسیار سخت و در مواقعی غیر ممکن است طراحی و ابداع روشهای عددی برای حل چنین معادلاتی بسیارحائز اهمیت میباشد. در این کار، اولا معادلات دیفرانسیل کسری جنبشی که برای نشان دادن فراینددینامیکی سیستمهای همیلتونی ارائه گردید، مورد مطالعه قرار میگیرد. ثانیا معادلات دیفرانسل کسریفرارفت – پخش با مشتق ریس در مکان با استفاده از درونیابی چندجملهایها بررسی خواهد گردید. در اینکار روشهای عددی مبتنی بر درونیابی چند جملهای طراحی خواهد گردید و پایداری و همگرایی روشها اثباتخواهد شد. در ادامه این روشها را برای حل معادلات دیفرانسیل جزئی با مشتق کسری بکار خواهیم برد.

Variant Title

روشهای عددی بر پایه چند جملهایهای درونیاب برای حل معادلات دیفرانسیل جزئی از مرتبه کسری با مشتق ریس مکانی

Subject Term

Fractional kinetics equation, Riesz space fractional advection-dispersion equation, Piecewise linear interpolation, Spline interpolants, Crank-Nicolson scheme, Matrix analysis method, Stability and Convergence.

Subject Term

معادله کسری کینیتیک، معادله کسری فرارفت- پخش، درونیابی خطی قطعهای، درونیابی اسپلاین، روش کرانک نیکلسون، روش آنالیز ماتریسی، پایداری و همگرایی.

Entry Element

Lateef Saeed,

Part of Name Other than Entry Element

Ihsan

Relator Code

Producer

Entry Element

Javidi,

Entry Element

Saedshoar Heris,

Part of Name Other than Entry Element

Mohammad

Part of Name Other than Entry Element

Mahdi

Relator Code

Thesis advisor

Relator Code

Consulting advisor

Entry Element

Tabriz

Country

ایران

Agency

Central Libarary of Tabriz University

Call Number

دکتری پایاننامه QA37/2.S2 1401

Electronic name

Ihsan Lateef Saeed

Contact for access assistance

عبادی

e

TL

276903

a

Y