eng
University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
2014-07-01
2
3
123
139
3006
Inverse Sturm-Liouville problems with transmission and spectral parameter boundary conditions
Mohammad Shahriari
shahriari@tabrizu.ac.ir
1
University of Maragheh
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).
http://cmde.tabrizu.ac.ir/article_3006_b58f6612cd4666d0abfa3f6283667255.pdf
Inverse Sturm-Liouville problem
Jump conditions
Green's function
Eigenparameter dependent condition
Transformation operator
eng
University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
2014-07-01
2
3
140
152
3007
An analytic study on the Euler-Lagrange equation arising in calculus of variations
Abbas Saadatmandi
a.saadatmandi@gmail.com
1
Tahereh Abdolahi-Niasar
abdolahi.tahereh@yahoo.com
2
University of Kashan, Kashan, Iran
University of Kashan, Kashan, Iran
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.
http://cmde.tabrizu.ac.ir/article_3007_36f175ff9db969636d2acf6818995572.pdf
Differential transformation method
Calculus of variation
Euler-Lagrange equation
Variational problems
eng
University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
2014-07-01
2
3
153
170
3267
A new fractional sub-equation method for solving the space-time fractional differential equations in mathematical physics
Mehmet Ekici
mehmet.ekici@bozok.edu.tr
1
Abdullah Sonmezoglu
abdullah.sonmezoglu@bozok.edu.tr
2
Elsayed M. E. Zayed
e.m.e.zayed@hotmail.com
3
Department of Mathematics, Faculty of Science and Arts, Bozok University, Yozgat, Turkey
Department of Mathematics, Faculty of Science and Arts, Bozok University, 66100 Yozgat, Turkey
Mathematics Department, Faculty of Science, Zagazig University, Zagazig, Egypt
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.
http://cmde.tabrizu.ac.ir/article_3267_6fb1541e5549a21636a8332f6f894880.pdf
Fractional sub-equation method
fractional partial differential equations
exact solutions
modified Riemann-Liouville derivative
eng
University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
2014-07-01
2
3
171
185
3281
New Solutions for Singular Lane-Emden Equations Arising in Astrophysics Based on Shifted Ultraspherical Operational Matrices of Derivatives
Waleed Abd- Elhameed
walee_9@yahoo.com
1
Youssri Youssri
youssri@sci.cu.edu.eg
2
Eid Doha
eiddoha@sci.cu.edu.eg
3
Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia
Department of Mathematics, Faculty of Science, Cairo University, Giza-Egypt
Department of Mathematics, Faculty of Science, Cairo University, Giza-Egypt
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.
http://cmde.tabrizu.ac.ir/article_3281_dd3a3207162ca5e8bb3b946eb9f13496.pdf
Ultraspherical polynomials
operational matrix of derivatives
Lane-Emden equations
isothermal gas spheres equation
eng
University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
2014-07-01
2
3
186
194
3318
Numerical inversion of Laplace transform via wavelet in ordinary differential equations
CHUN-HUI HSIAO
haar.wavelet@msa.hinet.net
1
No.101, Sec. 2, Jhongcheng Rd., Shihlin District, Taipei City 111, Taiwan, R.O.C.
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.
http://cmde.tabrizu.ac.ir/article_3318_45b84a55dd6bdc7e3ffbda5bbc7be1c0.pdf
Haar wavelet
Inverse Laplace transform
Operational matrix of integration
Haar product matrix
eng
University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
2014-07-01
2
3
195
204
3446
Numerical solution for boundary value problem of fractional order with approximate Integral and derivative
Abdol Ali Neamaty
aneamaty@yahoo.com
1
Bahram Agheli
b.agheli@yahoo.com
2
Mohammad Adabitabar
mohamadsadega@yahoo.com
3
Department of Mathematics, University of Mazandaran, Babolsar, Iran
Department of Mathematics, University of Mazandaran, Babolsar, Iran
Department of Mathematics, Qaemshahr Branch, Islamic Azad University, Qaemshahr, Iran
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.
http://cmde.tabrizu.ac.ir/article_3446_9fcbc0e8eb31a05b0a5e5b982d059e45.pdf
Boundary value problems of fractional order
Riemann-Liouville fractional derivative
Caputo fractional derivative
central difference