Limit cycle and bifurcation of nonlinear problems

He, Ji‐Huan

doi:10.1016/j.chaos.2005.03.007

Cited by 282 publications

(117 citation statements)

References 28 publications

Supporting

Mentioning

116

Contrasting

Unclassified

Order By: Relevance

“…The homotopy perturbation method proposed by He [2,26] is constantly being developed and applied to solve various nonlinear problems [3,4,7,11,[27][28][29][30][31][32]34]. Unlinke analytical perturbation methods, the homotopy-perturbation method does not depend on a small parameter which is difficult to find.…”

Section: Introductionmentioning

confidence: 99%

“…This new method was further developed and improved by He and applied to nonlinear oscillators with discontinuities [3], nonlinear wave equations [4], asymptotology [5], boundary value problem [6], limit cycle and bifurcation of nonlinear problems [7] and many other subjects. Thus He's method is a universal one which can solve various kinds of nonlinear equations.…”

Section: Introductionmentioning

confidence: 99%

“…In recent years, the application of the homotopy perturbation method (HPM) [5,7,30] in nonlinear problems has been developed by scientists and engineers, because this method deforms the difficult problem under study into a simple problem which is easy to solve. Most perturbation methods assume a small parameter exists, but most nonlinear problem have no small at all.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Numerical Solution Of 12th Order Boundary Value Problems By Using Homotopy Perturbation Method

Othman¹,

Mahdy²,

Farouk³

2010

J. Math. Computer Sci.

View full text Add to dashboard Cite

show abstract

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Numerical Solution Of 12th Order Boundary Value Problems By Using Homotopy Perturbation Method

Othman¹,

Mahdy²,

Farouk³

2010

J. Math. Computer Sci.

View full text Add to dashboard Cite

show abstract

Section: -Introductionmentioning

confidence: 99%

“…Also, in many works [17,18,19,20], the authors used ADM to found analytic and approximate solutions for different problems. In the same direction of modification, the HPM is active to find solutions for non-linear equations [10,[21][22][23][24][25][26][27][28][29][30].Depending on the above literature review for attempt of researchers to expand and developed ADM and HPM to solve linear and nonlinear boundary value problems, and depending on our simple information about applications of these methods to solve the problems that under consideration study, we did not find, if any, that is for problems are different from our problem in formulations and conditions. These information encourage us to suggest a new methodology for solving nonlinear problems.…”

mentioning

confidence: 99%

Splitting Decomposition Homotopy Perturbation Method To Solve One -Dimensional Navier -Stokes Equation

Al-Saif

Al‐Griffi

2017

JAM

View full text Add to dashboard Cite

I S S N 2347-1921 V o l u m e 13 N u m b e r 2 J o u r n a l o f A d v a n c e s i n M a t h e m a t i c s 7123 | P a g e A p r i l 2 0 1 7 w w w . c i r w o r l d . c o mSplitting decomposition homotopy perturbation method to solve onedimensional Navier-Stokes equation 1-IntroductionNavier-Stokes equations are non-linear partial differential equations that govern the incompressible fluid flow inside specific hollow as it is an equation of parabolic type and the non-linear degree is increased with the increase of Reynolds number . These equations names are taken from the two physicists Claude-Louis Navier and George Gabriel Stokes in the nineteenth century, and resulted from applying Newton second law on the movement of fluids supposing that stress of fluid is totaled of divergence of viscosity (proportional with velocity rate) and pressure. Also, these equations are considered as the most important physical equations which describe a large number of phenomena of different applications in many research fields that may be used in modeling weather, liquid flow in channels and pipes , gas flow round flying bodies, and movement of stars in the galaxy.Navier-Stokes equations are important mathematically, due to their wide applications, where to this day no one has succeeded in proving the existence of general solution or a permanent for Navier-Stokes equations( privately threedimensional). Therefore, this kind of problems is named as the existence and smooth flow of Navier-Stokes. During few last years, many researchers attempted to modify and extend these two methods; for example, Zhang [14 ] modified ADM to solve a class of non-linear boundary value problems. Jafari and Daftardar-Gejji [15] modified ADM to solve a set of non-linear equations led to find approximation solutions are better than those which were obtained by standrad method in measurements of convergent and accuracy. Luo [16] suggested active methods for ADM which is a two-steps Adomian decomposition method (TSADM) to reach the solution. TSADM reduces the repetitive of mathematical processes that are applied to find the solution and also he made comparison for the results. The results showed that TSADM is an active and efficient method which has high accuracy in finding solutions. Also, in many works [17,18,19,20], the authors used ADM to found analytic and approximate solutions for different problems. In the same direction of modification, the HPM is active to find solutions for non-linear equations [10,[21][22][23][24][25][26][27][28][29][30].Depending on the above literature review for attempt of researchers to expand and developed ADM and HPM to solve linear and nonlinear boundary value problems, and depending on our simple information about applications of these methods to solve the problems that under consideration study, we did not find, if any, that is for problems are different from our problem in formulations and conditions. These information encourage us to suggest a new methodology for solving nonlinear problems. The new methodology is con...

show abstract

A novel effective approach for solving nonlinear heat transfer equations

Aminikhah

Hemmatnezhad

2012

Heat Trans. Asian Res.

View full text Add to dashboard Cite

In this paper, a novel analytic technique, namely the Laplace transform new homotopy perturbation method (LTNHPM), is applied for solving the nonlinear differential equations arising in the field of heat transfer. This approach is a new modification to the homotopy perturbation method based on the Laplace transform. Unlike the previous approach implemented by the present authors for these problems, the present method does not consider the initial approximation as a power series. The nonlinear convective–radiative cooling equation and nonlinear equation of conduction heat transfer with the variable physical properties are chosen as illustrative examples. The exact solution has been found for the first case and for the others; results with remarkable accuracy have been achieved which verify the efficiency as well as accuracy of the presented approach. © 2012 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library (wileyonlinelibrary.com/journal/htj). DOI 10.1002/htj.20411

show abstract

Limit cycle and bifurcation of nonlinear problems

Cited by 282 publications

References 28 publications

Numerical Solution Of 12th Order Boundary Value Problems By Using Homotopy Perturbation Method

Numerical Solution Of 12th Order Boundary Value Problems By Using Homotopy Perturbation Method

Splitting Decomposition Homotopy Perturbation Method To Solve One -Dimensional Navier -Stokes Equation

A novel effective approach for solving nonlinear heat transfer equations

Contact Info

Product

Resources

About