𝔖 Bobbio Scriptorium
✦   LIBER   ✦

An optimal homotopy-analysis approach for strongly nonlinear differential equations

✍ Scribed by Shijun Liao

Publisher
Elsevier Science
Year
2010
Tongue
English
Weight
398 KB
Volume
15
Category
Article
ISSN
1007-5704

No coin nor oath required. For personal study only.

✦ Synopsis

In this paper, an optimal homotopy-analysis approach is described by means of the nonlinear Blasius equation as an example. This optimal approach contains at most three convergence-control parameters and is computationally rather efficient. A new kind of averaged residual error is defined, which can be used to find the optimal convergence-control parameters much more efficiently. It is found that all optimal homotopy-analysis approaches greatly accelerate the convergence of series solution. And the optimal approaches with one or two unknown convergence-control parameters are strongly suggested. This optimal approach has general meanings and can be used to get fast convergent series solutions of different types of equations with strong nonlinearity.

πŸ“œ SIMILAR VOLUMES

A one-step optimal homotopy analysis met
A one-step optimal homotopy analysis method for nonlinear differential equations
✍ Zhao Niu; Chun Wang πŸ“‚ Article πŸ“… 2010 πŸ› Elsevier Science 🌐 English βš– 327 KB

In this paper, a one-step optimal approach is proposed to improve the computational efficiency of the homotopy analysis method (HAM) for nonlinear problems. A generalized homotopy equation is first expressed by means of a unknown embedding function in Taylor series, whose coefficient is then determi

Reply to β€œComments on β€˜A one-step optima
Reply to β€œComments on β€˜A one-step optimal homotopy analysis method for nonlinear differential equations”’
✍ Chun Wang; Zhao Niu πŸ“‚ Article πŸ“… 2010 πŸ› Elsevier Science 🌐 English βš– 163 KB

## Marinca et al. [1] made some comments on our paper [2] and pointed out ''some fundamental mistakes and misinterpretations along with a false conclusion". Unfortunately, Marinca's comments are wrong. Here, we further reveal the essence of Marinca's approach, and point out the reason why their me

Comparison between homotopy analysis met
Comparison between homotopy analysis method and optimal homotopy asymptotic method for nth-order integro-differential equation
✍ M. Ghoreishi; A. I. B. MD. Ismail; A. K. Alomari πŸ“‚ Article πŸ“… 2011 πŸ› John Wiley and Sons 🌐 English βš– 439 KB

This paper presents general framework for solving the nth-order integro-differential equation using homotopy analysis method (HAM) and optimal homotopy asymptotic method (OHAM). OHAM is parameter free and can provide better accuracy over the HAM at the same order of approximation. Furthermore, in OH