scholarly journals A New Technique for Simulation the Zakharov–Kuznetsov Equation

2018 ◽  
Vol 14 (2) ◽  
pp. 7912-7920
Author(s):  
Mohammed Sabah Abdul-Wahab ◽  
A. S. J. Al-Saif
Keyword(s):  
Variational Iteration Method ◽  
Approximate Solutions ◽  
New Technique ◽  
Test Problems ◽  
Initial Condition ◽  
Two Dimensional ◽  
Analysis Method ◽  
Homotopy Analysis ◽  
A New Technique ◽  
Better Than

In this article, a new technique is proposed to simulated two-dimensional Zakharov–Kuznetsov equation with the initial condition. The idea of this technique is based on Taylors' series in its derivation. Two test problems are presented to illustrate the performance of the new scheme. Analytical approximate solutions that we obtain are compared with variational iteration method (VIM) and homotopy analysis method (HAM). The results show that the new scheme is efficient and better than the other methods in accuracy and convergence.

scholarly journals Constructing analytic solutions on the Tricomi equation

Open Physics ◽  
2018 ◽  
Vol 16 (1) ◽  
pp. 143-148 ◽  
Author(s):  
Emran Khoshrouye Ghiasi ◽  
Reza Saleh
Keyword(s):  
Homotopy Analysis Method ◽  
Series Solution ◽  
Variational Iteration Method ◽  
Approximate Solutions ◽  
Analytic Solutions ◽  
Analysis Method ◽  
Auxiliary Parameter ◽  
Tricomi Equation ◽  
Homotopy Analysis ◽  
Optimal Values

AbstractIn this paper, homotopy analysis method (HAM) and variational iteration method (VIM) are utilized to derive the approximate solutions of the Tricomi equation. Afterwards, the HAM is optimized to accelerate the convergence of the series solution by minimizing its square residual error at any order of the approximation. It is found that effect of the optimal values of auxiliary parameter on the convergence of the series solution is not negligible. Furthermore, the present results are found to agree well with those obtained through a closed-form equation available in the literature. To conclude, it is seen that the two are effective to achieve the solution of the partial differential equations.

scholarly journals A modification fractional variational iteration method for solving nonlinear gas dynamic and coupled KdV equations involving local fractional operators

2018 ◽  
Vol 22 (Suppl. 1) ◽  
pp. 165-175 ◽  
Author(s):  
Dumitru Baleanu ◽  
Hassan Jassim ◽  
Hasib Khan
Keyword(s):  
Iteration Method ◽  
Variational Iteration Method ◽  
Approximate Solutions ◽  
New Technique ◽  
Transform Method ◽  
Variational Iteration ◽  
Kdv Equations ◽  
Gas Dynamic ◽  
Coupled Kdv Equations ◽  
A New Technique

In this paper, we apply a new technique, namely local fractional variational iteration transform method on homogeneous/non-homogeneous non-linear gas dynamic and coupled KdV equations to obtain the analytical approximate solutions. The iteration procedure is based on local fractional derivative and integral operators. This method is the combination of the local fractional Laplace transform and variational iteration method. The method in general is easy to implement and yields good results. Illustrative examples are included to demonstrate the validity and applicability of the new technique.

scholarly journals Homotopy Analysis Method to Solve Two-Dimensional Nonlinear Volterra-Fredholm Fuzzy Integral Equations

2020 ◽  
Vol 4 (1) ◽  
pp. 9
Author(s):  
Atanaska Georgieva ◽  
Snezhana Hristova
Keyword(s):  
Integral Equation ◽  
Integral Equations ◽  
Homotopy Analysis Method ◽  
Approximate Solutions ◽  
Fredholm Integral Equations ◽  
Fuzzy Integral ◽  
Two Dimensional ◽  
Analysis Method ◽  
Homotopy Analysis ◽  
Fuzzy Solution

The main goal of the paper is to present an approximate method for solving of a two-dimensional nonlinear Volterra-Fredholm fuzzy integral equation (2D-NVFFIE). It is applied the homotopy analysis method (HAM). The studied equation is converted to a nonlinear system of Volterra-Fredholm integral equations in a crisp case. Approximate solutions of this system are obtained by the help with HAM and hence an approximation for the fuzzy solution of the nonlinear Volterra-Fredholm fuzzy integral equation is presented. The convergence of the proposed method is proved and the error estimate between the exact and the approximate solution is obtained. The validity and applicability of the proposed method is illustrated on a numerical example.

Analytical Approximations to Conservative Oscillators With Odd Nonlinearity Using the Variational Iteration Method

2012 ◽  
Vol 8 (1) ◽  
Author(s):  
A. Khosrozadeh ◽  
M. A. Hajabasi ◽  
H. R. Fahham
Keyword(s):  
Fourier Series ◽  
Iteration Method ◽  
Oscillation Amplitude ◽  
Variational Iteration Method ◽  
Approximate Solutions ◽  
New Technique ◽  
Variational Iteration ◽  
Analytical Approximations ◽  
A New Technique ◽  
Odd Nonlinearity

In this article, a new technique is introduced for establishing analytical approximate solutions to conservative oscillators with strong odd nonlinearity using the variational iteration method and the Fourier series. The illustrated examples show that only a few iterations can provide very accurate approximate solutions for the whole range of oscillation amplitude even for longer time ranges.

Two-Dimensional Local Deep-Level Transient Spectroscopy Imaging Using Super-Higher-Order Scanning Nonlinear Dielectric Microscopy

2016 ◽  
Author(s):  
N. Chinone ◽  
Y. Cho ◽  
R. Kosugi ◽  
Y. Tanaka ◽  
S. Harada ◽  
...  
Keyword(s):  
Deep Level Transient Spectroscopy ◽  
Deep Level ◽  
Higher Order ◽  
Trap Density ◽  
New Technique ◽  
Two Dimensional ◽  
Nonlinear Dielectric ◽  
Annealing Conditions ◽  
Transient Spectroscopy ◽  
A New Technique

Abstract A new technique for local deep level transient spectroscopy (DLTS) imaging using super-higher-order scanning nonlinear dielectric microscopy is proposed. Using this technique. SiCVSiC structure samples with different post oxidation annealing conditions were measured. We observed that the local DLTS signal decreases with post oxidation annealing (POA), which agrees with the well-known phenomena that POA reduces trap density. Furthermore, obtained local DLTS images had dark and bright areas, which is considered to show the trap distribution at/near SiCVSiC interface.

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