Title
Optimal Analytic Method For The Nonlinear Hasegawa-Mima Equation
Abstract
The Hasegawa-Mima equation is a nonlinear partial differential equation that describes the electric potential due to a drift wave in a plasma. In the present paper, we apply the method of homotopy analysis to a slightly more general Hasegawa-Mima equation, which accounts for hyper-viscous damping or viscous dissipation. First, we outline the method for the general initial/boundary value problem over a compact rectangular spatial domain. We use a two-stage method, where both the convergence control parameter and the auxiliary linear operator are optimally selected to minimize the residual error due to the approximation. To do the latter, we consider a family of operators parameterized by a constant which gives the decay rate of the solutions. After outlining the general method, we consider a number of concrete examples in order to demonstrate the utility of this approach. The results enable us to study properties of the initial/boundary value problem for the generalized Hasegawa-Mima equation. In several cases considered, we are able to obtain solutions with extremely small residual errors after relatively few iterations are computed (residual errors on the order of 10-15 are found in multiple cases after only three iterations). The results demonstrate that selecting a parameterized auxiliary linear operator can be extremely useful for minimizing residual errors when used concurrently with the optimal homotopy analysis method, suggesting that this approach can prove useful for a number of nonlinear partial differential equations arising in physics and nonlinear mechanics.
Publication Date
1-1-2014
Publication Title
European Physical Journal Plus
Volume
129
Issue
5
Number of Pages
-
Document Type
Article
Personal Identifier
scopus
DOI Link
https://doi.org/10.1140/epjp/i2014-14098-x
Copyright Status
Unknown
Socpus ID
84922569298 (Scopus)
Source API URL
https://api.elsevier.com/content/abstract/scopus_id/84922569298
STARS Citation
Baxter, Mathew; Van Gorder, Robert A.; and Vajravelu, Kuppalapalle, "Optimal Analytic Method For The Nonlinear Hasegawa-Mima Equation" (2014). Scopus Export 2010-2014. 9445.
https://stars.library.ucf.edu/scopus2010/9445