University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
2
3
2014
07
01
Inverse Sturm-Liouville problems with transmission and spectral parameter boundary conditions
123
139
EN
Mohammad
Shahriari
University of Maragheh
shahriari@tabrizu.ac.ir
This paper deals with the boundary value problem involving the differential equation ell y:=-y''+qy=lambda y, subject to the eigenparameter dependent boundary conditions along with the following discontinuity conditions y(d+0)=a y(d-0), y'(d+0)=ay'(d-0)+b y(d-0). In this problem q(x), d, a , b are real, qin L^2(0,pi), din(0,pi) and lambda is a parameter independent of x. By defining a new Hilbert space and using spectral data of a kind, it is developed the Hochestadt's result based on transformation operator for inverse Sturm-Liouville problem with parameter dependent boundary and discontinuous conditions. Furthermore, it is established a formula for q(x) - tilde{q}(x) in the finite interval, where tilde{q}(x) is an analogous function with q(x).
Inverse Sturm-Liouville problem,Jump conditions,Green's function,Eigenparameter dependent condition,Transformation operator
http://cmde.tabrizu.ac.ir/article_3006.html
http://cmde.tabrizu.ac.ir/article_3006_b58f6612cd4666d0abfa3f6283667255.pdf
University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
2
3
2014
07
01
An analytic study on the Euler-Lagrange equation arising in calculus of variations
140
152
EN
Abbas
Saadatmandi
University of Kashan, Kashan, Iran
a.saadatmandi@gmail.com
Tahereh
Abdolahi-Niasar
University of Kashan, Kashan, Iran
abdolahi.tahereh@yahoo.com
The Euler-Lagrange equation plays an important role in the minimization problems of the calculus of variations. This paper employs the differential transformation method (DTM) for finding the solution of the Euler-Lagrange equation which arise from problems of calculus of variations. DTM provides an analytical solution in the form of an infinite power series with easily computable components. Several illustrative examples are given to demonstrate the effectiveness of the present method.
Differential transformation method,Calculus of variation,Euler-Lagrange equation,Variational problems
http://cmde.tabrizu.ac.ir/article_3007.html
http://cmde.tabrizu.ac.ir/article_3007_36f175ff9db969636d2acf6818995572.pdf
University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
2
3
2014
07
01
A new fractional sub-equation method for solving the space-time fractional differential equations in mathematical physics
153
170
EN
Mehmet
Ekici
Department of Mathematics, Faculty of Science and Arts, Bozok University, Yozgat, Turkey
mehmet.ekici@bozok.edu.tr
Abdullah
Sonmezoglu
Department of Mathematics, Faculty of Science and Arts, Bozok University, 66100 Yozgat, Turkey
abdullah.sonmezoglu@bozok.edu.tr
Elsayed M. E.
Zayed
Mathematics Department, Faculty of Science, Zagazig University, Zagazig, Egypt
e.m.e.zayed@hotmail.com
In this paper, a new fractional sub-equation method is proposed for finding exact solutions of fractional partial differential equations (FPDEs) in the sense of modified Riemann-Liouville derivative. With the aid of symbolic computation, we choose the space-time fractional Zakharov-Kuznetsov-Benjamin-Bona-Mahony (ZKBBM) equation in mathematical physics with a source to illustrate the validity and advantages of the novel method. As a result, some new exact solutions including solitary wave solutions and periodic wave solutions are successfully obtained. The proposed approach can also be applied to other nonlinear FPDEs arising in mathematical physics.
Fractional sub-equation method,fractional partial differential equations,exact solutions,modified Riemann-Liouville derivative
http://cmde.tabrizu.ac.ir/article_3267.html
http://cmde.tabrizu.ac.ir/article_3267_6fb1541e5549a21636a8332f6f894880.pdf
University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
2
3
2014
07
01
New Solutions for Singular Lane-Emden Equations Arising in Astrophysics Based on Shifted Ultraspherical Operational Matrices of Derivatives
171
185
EN
Waleed
M.
Abd- Elhameed
Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia
walee_9@yahoo.com
Youssri
Youssri
Department of Mathematics, Faculty of Science, Cairo University, Giza-Egypt
youssri@sci.cu.edu.eg
Eid
H.
Doha
Department of Mathematics, Faculty of Science, Cairo University, Giza-Egypt
eiddoha@sci.cu.edu.eg
In this paper, the ultraspherical operational matrices of derivatives are constructed. Based on these operational matrices, two numerical algorithms are presented and analyzed for obtaining new approximate spectral solutions of a class of linear and nonlinear Lane-Emden type singular initial value problems. The basic idea behind the suggested algorithms is basically built on transforming the equations with their initial conditions into systems of linear or nonlinear algebraic equations which can be solved by using suitable numerical solvers. The Legendre and first and second kind Chebyshev operational matrices of derivatives can be deduced as special cases of the constructed operational matrices. For the sake of testing the validity and applicability of the suggested numerical algorithms, three illustrative examples are presented.
Ultraspherical polynomials,operational matrix of derivatives,Lane-Emden equations,isothermal gas spheres equation
http://cmde.tabrizu.ac.ir/article_3281.html
http://cmde.tabrizu.ac.ir/article_3281_dd3a3207162ca5e8bb3b946eb9f13496.pdf
University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
2
3
2014
07
01
Numerical inversion of Laplace transform via wavelet in ordinary differential equations
186
194
EN
CHUN-HUI
HSIAO
No.101, Sec. 2, Jhongcheng Rd., Shihlin District, Taipei City 111, Taiwan, R.O.C.
haar.wavelet@msa.hinet.net
This paper presents a rational Haar wavelet operational method for solving the inverse Laplace transform problem and improves inherent errors from irrational Haar wavelet. The approach is thus straightforward, rather simple and suitable for computer programming. We define that $P$ is the operational matrix for integration of the orthogonal Haar wavelet. Simultaneously, simplify the formulaes of listing table to a minimum expression and obtain the optimal operation speed. The local property of Haar wavelet is fully applied to shorten the calculation process in the task.
Haar wavelet,Inverse Laplace transform,Operational matrix of integration,Haar product matrix
http://cmde.tabrizu.ac.ir/article_3318.html
http://cmde.tabrizu.ac.ir/article_3318_45b84a55dd6bdc7e3ffbda5bbc7be1c0.pdf
University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
2
3
2014
07
01
Numerical solution for boundary value problem of fractional order with approximate Integral and derivative
195
204
EN
Abdol Ali
Neamaty
Department of Mathematics, University of Mazandaran, Babolsar, Iran
aneamaty@yahoo.com
Bahram
Agheli
Department of Mathematics, University of Mazandaran, Babolsar, Iran
b.agheli@yahoo.com
Mohammad
Adabitabar
Department of Mathematics, Qaemshahr Branch, Islamic Azad University, Qaemshahr, Iran
mohamadsadega@yahoo.com
Approximating the solution of differential equations of fractional order is necessary because fractional differential equations have extensively been used in physics, chemistry as well as engineering fields. In this paper with central difference approximation and Newton Cots integration formula, we have found approximate solution for a class of boundary value problems of fractional order. Three numerical examples are presented to describe the fractional usefulness of the suggested method.
Boundary value problems of fractional order,Riemann-Liouville fractional derivative,Caputo fractional derivative,central difference
http://cmde.tabrizu.ac.ir/article_3446.html
http://cmde.tabrizu.ac.ir/article_3446_9fcbc0e8eb31a05b0a5e5b982d059e45.pdf