Homotopy Analysis Method

Homotopy analysis method (HAM) is one of the well‐known semi‐analytical methods for solving various types of linear and nonlinear differential equations (ordinary as well as partial). This method is based on coupling of the traditional perturbation method and homotopy in topolo...

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Bibliographic Details
Published in:Advanced Numerical and Semi-Analytical Methods for Differential Equations pp. 149 - 156
Main Authors: Chakraverty, Snehashish, Mahato, Nisha, Karunakar, Perumandla, Dilleswar Rao, Tharasi
Format: Book Chapter
Language:English
Published: United States Wiley 2019
John Wiley & Sons, Incorporated
John Wiley & Sons, Inc
Edition:1
Subjects:
convergence control parameter
homotopy analysis method
linear partial differential equation
nonlinear partial differential equation
semi‐analytical methods
Couplings
Topology
Perturbation methods
Strain
Convergence
ISBN:9781119423423, 1119423422
Online Access:Get full text
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Summary:Homotopy analysis method (HAM) is one of the well‐known semi‐analytical methods for solving various types of linear and nonlinear differential equations (ordinary as well as partial). This method is based on coupling of the traditional perturbation method and homotopy in topology. By this method one may get exact solution or a power series solution which converges in general to exact solution. The HAM consists of convergence control parameter, which controls the convergent region and rate of convergence of the series solution. This chapter applies the present method to solve a linear partial differential equation in a numerical example and a nonlinear partial differential equation in another numerical example. It may be noted that the HAM not only produces approximate convergent series solution but it can also give exact solution depending on the considered problem with proper control parameter.
ISBN:9781119423423
1119423422
DOI:10.1002/9781119423461.ch14