Homotopy Analysis And Legendre Multi-Wavelets Methods For Solving Integral Equations
Due to the ability of function representation, hybrid functions and wavelets have a special position in research. In this thesis, we state elementary definitions, then we introduce hybrid functions and some wavelets such as Haar, Daubechies, Cheby- shev, sine-cosine and linear Legendre multi wave...
محفوظ في:
| المؤلف الرئيسي: | |
|---|---|
| التنسيق: | أطروحة |
| اللغة: | English English |
| منشور في: |
2009
|
| الموضوعات: | |
| الوصول للمادة أونلاين: | http://psasir.upm.edu.my/id/eprint/12370/1/IPM_2009_12A.pdf |
| الوسوم: |
إضافة وسم
لا توجد وسوم, كن أول من يضع وسما على هذه التسجيلة!
|
| id |
my-upm-ir.12370 |
|---|---|
| record_format |
uketd_dc |
| spelling |
my-upm-ir.123702013-05-27T07:51:53Z Homotopy Analysis And Legendre Multi-Wavelets Methods For Solving Integral Equations 2009-12 Vahdati, Saeed Due to the ability of function representation, hybrid functions and wavelets have a special position in research. In this thesis, we state elementary definitions, then we introduce hybrid functions and some wavelets such as Haar, Daubechies, Cheby- shev, sine-cosine and linear Legendre multi wavelets. The construction of most wavelets are based on stepwise functions and the comparison between two categories of wavelets will become easier if we have a common construction of them. The properties of the Floor function are used to and a function which is one on the interval [0; 1) and zero elsewhere. The suitable dilation and translation parameters lead us to get similar function corresponding to the interval [a; b). These functions and their combinations enable us to represent the stepwise functions as a function of floor function. We have applied this method on Haar wavelet, Sine-Cosine wavelet, Block - Pulse functions and Hybrid Fourier Block-Pulse functions to get the new representations of these functions. The main advantage of the wavelet technique for solving a problem is its ability to transform complex problems into a system of algebraic equations. We use the Legendre multi-wavelets on the interval [0; 1) to solve the linear integro-differential and Fredholm integral equations of the second kind. We also use collocation points and linear legendre multi wavelets to solve an integro-differential equation which describes the charged particle motion for certain configurations of oscillating magnetic fields. Illustrative examples are included to reveal the sufficiency of the technique. In linear integro-differential equations and Fredholm integral equations of the second kind cases, comparisons are done with CAS wavelets and differential transformation methods and it shows that the accuracy of these results are higher than them. Homotopy Analysis Method (HAM) is an analytic technique to solve the linear and nonlinear equations which can be used to obtain the numerical solution too. We extend the application of homotopy analysis method for solving Linear integro- differential equations and Fredholm and Volterra integral equations. We provide some numerical examples to demonstrate the validity and applicability of the technique. Numerical results showed the advantage of the HAM over the HPM, SCW, LLMW and CAS wavelets methods. For future studies, some problems are proposed at the end of this thesis. Homotopy theory Wavelets (Mathematics) 2009-12 Thesis http://psasir.upm.edu.my/id/eprint/12370/ http://psasir.upm.edu.my/id/eprint/12370/1/IPM_2009_12A.pdf application/pdf en public phd doctoral Universiti Putra Malaysia Homotopy theory Wavelets (Mathematics) Institute For Mathematical Research English |
| institution |
Universiti Putra Malaysia |
| collection |
PSAS Institutional Repository |
| language |
English English |
| topic |
Homotopy theory Wavelets (Mathematics) |
| spellingShingle |
Homotopy theory Wavelets (Mathematics) Vahdati, Saeed Homotopy Analysis And Legendre Multi-Wavelets Methods For Solving Integral Equations |
| description |
Due to the ability of function representation, hybrid functions and wavelets have a
special position in research. In this thesis, we state elementary definitions, then we
introduce hybrid functions and some wavelets such as Haar, Daubechies, Cheby-
shev, sine-cosine and linear Legendre multi wavelets. The construction of most
wavelets are based on stepwise functions and the comparison between two categories of wavelets will become easier if we have a common construction of them.
The properties of the Floor function are used to and a function which is one on the
interval [0; 1) and zero elsewhere. The suitable dilation and translation parameters
lead us to get similar function corresponding to the interval [a; b). These functions
and their combinations enable us to represent the stepwise functions as a function of
floor function. We have applied this method on Haar wavelet, Sine-Cosine wavelet,
Block - Pulse functions and Hybrid Fourier Block-Pulse functions to get the new
representations of these functions.
The main advantage of the wavelet technique for solving a problem is its ability
to transform complex problems into a system of algebraic equations. We use the Legendre multi-wavelets on the interval [0; 1) to solve the linear integro-differential
and Fredholm integral equations of the second kind. We also use collocation points
and linear legendre multi wavelets to solve an integro-differential equation which describes the charged particle motion for certain configurations of oscillating magnetic
fields. Illustrative examples are included to reveal the sufficiency of the technique.
In linear integro-differential equations and Fredholm integral equations of the second
kind cases, comparisons are done with CAS wavelets and differential transformation
methods and it shows that the accuracy of these results are higher than them.
Homotopy Analysis Method (HAM) is an analytic technique to solve the linear
and nonlinear equations which can be used to obtain the numerical solution too.
We extend the application of homotopy analysis method for solving Linear integro-
differential equations and Fredholm and Volterra integral equations. We provide
some numerical examples to demonstrate the validity and applicability of the technique. Numerical results showed the advantage of the HAM over the HPM, SCW,
LLMW and CAS wavelets methods. For future studies, some problems are proposed
at the end of this thesis. |
| format |
Thesis |
| qualification_name |
Doctor of Philosophy (PhD.) |
| qualification_level |
Doctorate |
| author |
Vahdati, Saeed |
| author_facet |
Vahdati, Saeed |
| author_sort |
Vahdati, Saeed |
| title |
Homotopy Analysis And Legendre Multi-Wavelets Methods For Solving Integral Equations |
| title_short |
Homotopy Analysis And Legendre Multi-Wavelets Methods For Solving Integral Equations |
| title_full |
Homotopy Analysis And Legendre Multi-Wavelets Methods For Solving Integral Equations |
| title_fullStr |
Homotopy Analysis And Legendre Multi-Wavelets Methods For Solving Integral Equations |
| title_full_unstemmed |
Homotopy Analysis And Legendre Multi-Wavelets Methods For Solving Integral Equations |
| title_sort |
homotopy analysis and legendre multi-wavelets methods for solving integral equations |
| granting_institution |
Universiti Putra Malaysia |
| granting_department |
Institute For Mathematical Research |
| publishDate |
2009 |
| url |
http://psasir.upm.edu.my/id/eprint/12370/1/IPM_2009_12A.pdf |
| _version_ |
1747811359283740672 |