scholarly journals NUMERICAL EXPERIMENTS FOR NONLINEAR BURGER’S PROBLEM

2021 ◽  
Vol 16 (11) ◽  
Author(s):  
Jawad Kadhim Tahir
Keyword(s):  
Variational Approach ◽  
Numerical Experiments ◽  
Computational Experiments ◽  
Compact Form ◽  
Exact Linearization ◽  
Nonlinear Solution ◽  
Transformation Approach

The article contains the results of computational experiments for the non-homogeneous Burger’s problem and finding its solution by using the non-classical variational-Cole-Hopf transformation approach. On using exact linearization via Cole-Hopf transformation, as well as the application of the non-classical variational approach, then the non-homogeneous Burger’s problem has been solved. The solution which is obtained by this approach is in a compact form so that the original nonlinear solution is easy to be approximated. The accuracy of this method is dependent on the types of selected basis and its number.

scholarly journals A variational approach to a BVP arising in the modelling of electrically conducting solids

2013 ◽  
Vol 3 (1) ◽  
Author(s):  
Suheil Khuri ◽  
Abdul-Majid Wazwaz
Keyword(s):  
Exact Solution ◽  
Boundary Value Problem ◽  
Uniform Convergence ◽  
Variational Approach ◽  
Numerical Experiments ◽  
Nonlinear Boundary ◽  
Positive Temperature ◽  
Temperature Dependent ◽  
Electrically Conducting ◽  
Dependent Sources

AbstractThe purpose of this paper is to apply an amended variational scheme, based on an adapted domain decomposition, for the solution of a second-order nonlinear boundary value problem that arises in applications involving the diffusion of heat generated by positive temperature dependent sources. The underlying idea of this approach is to decompose the original interval prior to the implementation of the iterative variational approach in order to improve the accuracy and acquire uniform convergence to the exact solution over the entire domain. Convergence analysis is given and then numerical experiments are carried out to make obvious the convergence, accuracy and efficient applicability of the method.

scholarly journals Nonconvex regularization for blurred images with Cauchy noise

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Xiao Ai ◽  
Guoxi Ni ◽  
Tieyong Zeng
Keyword(s):  
Minimization Problem ◽  
Variational Approach ◽  
Numerical Experiments ◽  
Alternating Direction Method ◽  
Wavelet Frame ◽  
Alternating Direction ◽  
Nonconvex Regularization ◽  
Blurred Images ◽  
Different Levels

<p style='text-indent:20px;'>In this paper, we propose a nonconvex regularization model for images damaged by Cauchy noise and blur. This model is based on the method of the total variational proposed by Federica, Dong and Zeng [SIAM J. Imaging Sci.(2015)], where a variational approach for restoring blurred images with Cauchy noise is used. Here we consider the nonconvex regularization, namely a weighted difference of <inline-formula><tex-math id="M1">\begin{document}$ l_1 $\end{document}</tex-math></inline-formula>-norm and <inline-formula><tex-math id="M2">\begin{document}$ l_2 $\end{document}</tex-math></inline-formula>-norm coupled with wavelet frame, the alternating direction method of multiplier is carried out for this minimization problem, we describe the details of the algorithm and prove its convergence. Numerical experiments are tested by adding different levels of noise and blur, results show that our method can denoise and deblur the image better.</p>

Quasi Static Analysis of Anti-Plane Shear Crack

2012 ◽  
Vol 232 ◽  
pp. 92-96 ◽  
Author(s):  
Hamdi Hentati ◽  
Radhi Abdelmoula ◽  
Aref Maalej ◽  
Khalil Maalej
Keyword(s):  
Crack Propagation ◽  
Variational Approach ◽  
Numerical Experiments ◽  
Crack Path ◽  
Shear Crack ◽  
Initial Crack ◽  
Kinetic Term ◽  
Plane Shear ◽  
Standard Linear ◽  
Lagrange Finite Element

Fracture mechanics has been revisited by proposing different models of quasi static brittle fracture. In this work, the problem of the quasi static crack propagation is based on variational approach. It requires no prior knowledge of the crack path or of its topology. Moreover, it is capable of modeling crack initiation. In the numerical experiments, we use a standard linear (P1) Lagrange finite element method for discretization. We perform numerical simulations of a piece of brittle material without initial crack. An alternate minimizations algorithm is used. Based on these numerical results, we determine the influence of numerical parameters on the evolution of energies and crack propagation. We show also the necessity of considering the kinetic term and the crack propagation becomes dynamic.

Zonal and tesseral harmonic perturbations of an artificial satellite

1966 ◽  
Vol 25 ◽  
pp. 323-325 ◽  
Author(s):  
B. Garfinkel
Keyword(s):  
Angular Velocity ◽  
Spherical Harmonics ◽  
Artificial Satellite ◽  
Compact Form ◽  
Earth’S Rotation ◽  
Earth's Rotation ◽  
Secular Variations ◽  
Tesseral Harmonics

The paper extends the known solution of the Main Problem to include the effects of the higher spherical harmonics of the geopotential. The von Zeipel method is used to calculate the secular variations of orderJmand the long-periodic variations of ordersJm/J2andnJm,λ/ω. HereJmandJm,λare the coefficients of the zonal and the tesseral harmonics respectively, withJm,0=Jm, andωis the angular velocity of the Earth's rotation. With the aid of the theory of spherical harmonics the results are expressed in a most compact form.

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