Variational iteration algorithm-II for solving linear and non-linear ODEs

2012 ◽  
Vol 7 (25) ◽  
Author(s):  
Y. Khan
Keyword(s):  
Iteration Algorithm ◽  
Variational Iteration ◽  
Non Linear ◽  
Linear Odes

scholarly journals Local fractional variational iteration algorithm iii for the diffusion model associated with non-differentiable heat transfer

2016 ◽  
Vol 20 (suppl. 3) ◽  
pp. 781-784 ◽  
Author(s):  
Zhi-Jun Meng ◽  
Yao-Ming Zhou ◽  
Huan-Qing Wang
Keyword(s):  
Heat Transfer ◽  
Diffusion Equation ◽  
Diffusion Model ◽  
Fractional Diffusion ◽  
Cantor Sets ◽  
Fractional Diffusion Equation ◽  
Iteration Algorithm ◽  
Variational Iteration

This paper addresses a new application of the local fractional variational iteration algorithm III to solve the local fractional diffusion equation defined on Cantor sets associated with non-differentiable heat transfer.

scholarly journals Modified Variational Iteration Algorithm-II: Convergence and Applications to Diffusion Models

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-14 ◽  
Author(s):  
Hijaz Ahmad ◽  
Tufail A. Khan ◽  
Predrag S. Stanimirović ◽  
Yu-Ming Chu ◽  
Imtiaz Ahmad
Keyword(s):  
Differential Equations ◽  
Numerical Solutions ◽  
Nonlinear Models ◽  
Nonlinear Differential Equations ◽  
Variational Iteration Method ◽  
Iteration Algorithm ◽  
Compact Finite Difference Method ◽  
Variational Iteration ◽  
Linear And Nonlinear ◽  
The Stability

Variational iteration method has been extensively employed to deal with linear and nonlinear differential equations of integer and fractional order. The key property of the technique is its ability and flexibility to investigate linear and nonlinear models conveniently and accurately. The current study presents an improved algorithm to the variational iteration algorithm-II (VIA-II) for the numerical treatment of diffusion as well as convection-diffusion equations. This newly introduced modification is termed as the modified variational iteration algorithm-II (MVIA-II). The convergence of the MVIA-II is studied in the case of solving nonlinear equations. The main advantage of the MVIA-II improvement is an auxiliary parameter which makes sure a fast convergence of the standard VIA-II iteration algorithm. In order to verify the stability, accuracy, and computational speed of the method, the obtained solutions are compared numerically and graphically with the exact ones as well as with the results obtained by the previously proposed compact finite difference method and second kind Chebyshev wavelets. The comparison revealed that the modified version yields accurate results, converges rapidly, and offers better robustness in comparison with other methods used in the literature. Moreover, the basic idea depicted in this study is relied upon the possibility of the MVIA-II being utilized to handle nonlinear differential equations that arise in different fields of physical and biological sciences. A strong motivation for such applications is the fact that any discretization, transformation, or any assumptions are not required for this proposed algorithm in finding appropriate numerical solutions.

scholarly journals An Aproximation to Solution of Space and Time Fractional Telegraph Equations by the Variational Iteration Method

2012 ◽  
Vol 2012 ◽  
pp. 1-2 ◽  
Author(s):  
Ji-Huan He
Keyword(s):  
Iteration Method ◽  
Variational Iteration Method ◽  
Iteration Algorithm ◽  
Effective Algorithm ◽  
Variational Iteration ◽  
Space And Time ◽  
Telegraph Equations

Sevimlican suggested an effective algorithm for space and time fractional telegraph equations by the variational iteration method. This paper shows that algorithm can be updated by either variational iteration algorithm-II or the fractional variational iteration method.

Study of the dynamics of rotor-spun composite yarn spinning process in forced vibration

2011 ◽  
Vol 82 (3) ◽  
pp. 255-258 ◽  
Author(s):  
Naeem Faraz ◽  
Yasir Khan
Keyword(s):  
Forced Vibration ◽  
Iteration Method ◽  
Variational Iteration Method ◽  
Variational Iteration ◽  
Composite Yarn ◽  
Force Vibration ◽  
Non Linear ◽  
Spinning Process ◽  
Linear Force

The non-linear force vibration oscillator is established for the rotor-spun composite yarn spinning process. The variational iteration method is used to calculate the approximate oscillating periods in the vertical and horizontal directions. Thecondition for resonance is obtained.

scholarly journals The local fractional variational iteration method a promising technology for fractional calculus

2020 ◽  
Vol 24 (4) ◽  
pp. 2605-2614 ◽  
Author(s):  
Yong-Ju Yang
Keyword(s):  
Fractional Calculus ◽  
Iteration Method ◽  
Variational Iteration Method ◽  
Initial Solution ◽  
Iteration Algorithm ◽  
Promising Technology ◽  
Variational Iteration ◽  
Sumudu Transform

In order to make the local variational iteration algorithm converge faster and more effective, the Sumudu transform is adopted and a proper initial solution is chosen. Some examples are given to show that the presented method is reliable, efficient and easy to implement from a computational viewpoint.

scholarly journals Passive control of magneto-nanomaterials transient flow subject to non-linear thermal radiation

2021 ◽  
pp. 169-169
Author(s):  
Ikram Ullah ◽  
Sayed Shah ◽  
Gul Zaman ◽  
Taseer Muhammad ◽  
Zakir Hussain
Keyword(s):  
Thermal Radiation ◽  
Passive Control ◽  
Stretching Sheet ◽  
Transient Flow ◽  
Brownian Diffusion ◽  
Convection Flow ◽  
Stretching Surface ◽  
Surface Drag ◽  
Non Linear ◽  
Linear Odes

Present investigation is concerned with mixed convection flow of Williamson nanoliquid over an unsteady slandering stretching sheet. Aspects of non-linear thermal radiation, Brownian diffusion and thermophoresis effects are addressed. Non-linear stretching surface of varying thickness induce the flow. Novel features of combined zero mass flux and convective conditions are accounted. Use of appropriate transformations results into the non-linear ODEs. Computations for the convergent solutions are provided. Graphs are designed for interpretations to quantities. Nusselt number and surface drag are computationally inspected. Our computed results indicate that attributes of nanoparticles and non-linear thermal radiation enhance the temperature distribution.

scholarly journals Flow* 1.2: More Effective to Play with Hybrid Systems

10.29007/1w4t ◽  
2018 ◽  
Author(s):  
Xin Chen ◽  
Sriram Sankaranarayanan ◽  
Erika Abraham
Keyword(s):  
Hybrid Systems ◽  
Non Linear ◽  
Efficient Scheme ◽  
Linear Odes

This paper gives a brief overview of the new features introduced in the latest version of the tool Flow*. We mainly describe the new efficient scheme for integrating linear ODEs. We show that it can efficiently handle the challenging benchmarks on which, to the best of our knowledge, only SpaceEx works. Moreover, it is also possible to extend the method to deal with unbounded initial sets. A comparison between Flow* 1.2 and SpaceEx on those benchmarks is given. Besides, we also investigate the scalability Flow* 1.2 based on our non-linear line circuit benchmarks.

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