University of TabrizComputational Methods for Differential Equations2345-39822420141001Existence and uniqueness of solutions for p-laplacian fractional order boundary value problems2052153138ENRahmatAli KhanDepartment of Mathematics, University of Malaknd at Chakdara Dir Lower, Khybar Pakhtunkhwa, PakistanAzizKhanUniversity of Peshawar, PakistanJournal Article20141109In this paper, we study sufficient conditions for existence and uniqueness of solutions of three point boundary vale problem for p-Laplacian fractional order differential equations. We use Schauder's fixed point theorem for existence of solutions and concavity of the operator for uniqueness of solution. We include some examples to show the applicability of our results.https://cmde.tabrizu.ac.ir/article_3138_d0d51e21fca62f083313ef3d8e8382a6.pdfUniversity of TabrizComputational Methods for Differential Equations2345-39822420141001The B"{a}cklund transformation method of Riccati equation to coupled Higgs field and Hamiltonian amplitude equations2162263316ENAhmad HasanArnousDepartment of Engineering Mathematics and Physics, Higher Institute of Engineering, El Shorouk, Cairo, EgyptMohammadMirzazadehDepartment of Mathematics, Faculty of Mathematical Sciences, University of Guilan, Rasht, IranMostafaEslamiDepartment of Mathematics,
Faculty of Mathematical Sciences,
University of Mazandaran, Babolsar, Iran0000-0001-6168-7916Journal Article20141225In this paper, we establish new exact solutions for some complex nonlinear wave equations. The B"{a}cklund transformation method of Riccati equation is used to construct exact solutions of the Hamiltonian amplitude equation and the coupled Higgs field equation. This method presents a wide applicability to handling nonlinear wave equations. These equations play a very important role in mathematical physics and engineering sciences. Obtained solutions may also be important of significance for the explanation of some practical physical problems.https://cmde.tabrizu.ac.ir/article_3316_ee955e00f9d31c2df0030b5e9eb6adc2.pdfUniversity of TabrizComputational Methods for Differential Equations2345-39822420141001Topological soliton solutions of the some nonlinear partial differential equations2272423169ENOzkanGunerCankiri Karatekin University, Faculty of Economics and Administrative Sciences,
Department of International Trade, Cankiri-TURKEYJournal Article20141009In this paper, we obtained the 1-soliton solutions of the symmetric regularized long wave (SRLW) equation and the (3+1)-dimensional shallow water wave equations. Solitary wave ansatz method is used to carry out the integration of the equations and obtain topological soliton solutions The physical parameters in the soliton solutions are obtained as functions of the dependent coefficients. Note that, this method is always useful and desirable to construct exact solutions especially soliton-type envelope for the understanding of most nonlinear physical phenomena.https://cmde.tabrizu.ac.ir/article_3169_3e9ca9ba1422f83c2e9e20459cfdf8e4.pdfUniversity of TabrizComputational Methods for Differential Equations2345-39822420141001Generalized B-spline functions method for solving optimal control problems2432553772ENYousefEdrisi TabrizDepartment of Mathematics,
Payame Noor University,
PO BOX 19395-3697, Tehran, IranAghilehHeydariDepartment of Mathematics,
Payame Noor University,
PO BOX 19395-3697, Tehran, IranJournal Article20150620In this paper we introduce a numerical approach that solves optimal control problems (OCPs) using collocation methods. This approach is based upon B-spline functions. The derivative matrices between any two families of B-spline functions are utilized to reduce the solution of OCPs to the solution of nonlinear optimization problems. Numerical experiments confirm our heoretical findings.https://cmde.tabrizu.ac.ir/article_3772_469ce62234092e58427d577e03b4b0d4.pdfUniversity of TabrizComputational Methods for Differential Equations2345-39822420141001Positivity-preserving nonstandard finite difference Schemes for simulation of advection-diffusion reaction equations2562673583ENMohammadMehdizadeh KhalsaraeiFaculty of Mathematical Science, University of Maragheh, Maragheh, IranRezaShokri JahandiziFaculty of Mathematical Science, University of Maragheh, Maragheh, IranJournal Article20150201Systems in which reaction terms are coupled to diffusion and advection transports arise in a wide range of chemical engineering applications, physics, biology and environmental. In these cases, the components of the unknown can denote concentrations or population sizes which represent quantities and they need to remain positive. Classical finite difference schemes may produce numerical drawbacks such as spurious oscillations and negative solutions because of truncation errors and may then become unstable. we propose a new scheme that guarantees a smooth numerical solution, free of spurious oscillations and satisfies the positivity requirement, as is demanded for the advection-diffusion reaction equations. The method is applicable to both advection and diffusion dominated problems. We give some examples from different applications.https://cmde.tabrizu.ac.ir/article_3583_bfed57f3653505f17e60608b463669be.pdfUniversity of TabrizComputational Methods for Differential Equations2345-39822420141001Fractional type of flatlet oblique multiwavelet for solving fractional differential and integro-differential equations2682823834ENMohammadrezaAhmadi DaraniFaculty of mathematical Sciences,
Shahrekord University, P. O. Box 115, Shahrekord, Iran.ShirinBagheriFaculty of Basic Sciences, Islamic Azad University, Science and Research Branch,
P. O. Box 14515/775, Tehran, Iran.Journal Article20150612The construction of fractional type of flatlet biorthogonal multiwavelet system is investigated in this paper. We apply this system as basis functions to solve the fractional differential and integro-differential equations. Biorthogonality and high vanishing moments of this system are two major properties which lead to the good approximation for the solutions of the given problems. Some test problems are discussed at the end of paper to show the efficiency of the proposed method.https://cmde.tabrizu.ac.ir/article_3834_bb3f883a1e0a93f9f79e70f8f6790c93.pdf