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The Resource Homotopy analysis method in nonlinear differential equations, Shijun Liao

Homotopy analysis method in nonlinear differential equations, Shijun Liao

Label
Homotopy analysis method in nonlinear differential equations
Title
Homotopy analysis method in nonlinear differential equations
Statement of responsibility
Shijun Liao
Creator
Subject
Language
eng
Summary
Annotation
Cataloging source
GW5XE
http://library.link/vocab/creatorDate
1963-
http://library.link/vocab/creatorName
Liao, Shijun
Dewey number
515/.355
Illustrations
illustrations
Index
index present
LC call number
QA372
LC item number
.L53 2012
Literary form
non fiction
Nature of contents
  • dictionaries
  • bibliography
NLM call number
Online Book
http://library.link/vocab/subjectName
  • Differential equations, Nonlinear
  • Differential equations, Partial
  • Homotopy theory
  • Mathematical analysis
  • Mathematics
  • MATHEMATICS
  • Differential equations, Nonlinear
  • Differential equations, Partial
  • Homotopy theory
  • Mathematical analysis
Summary expansion
"Homotopy Analysis Method in Nonlinear Differential Equations" presents the latest developments and applications of the analytic approximation method for highly nonlinear problems, namely the homotopy analysis method (HAM). Unlike perturbation methods, the HAM has nothing to do with small/large physical parameters. In addition, it provides great freedom to choose the equation-type of linear sub-problems and the base functions of a solution. Above all, it provides a convenient way to guarantee the convergence of a solution. This book consists of three parts. Part I provides its basic ideas and theoretical development. Part II presents the HAM-based Mathematica package BVPh 1.0 for nonlinear boundary-value problems and its applications. Part III shows the validity of the HAM for nonlinear PDEs, such as the American put option and resonance criterion of nonlinear travelling waves. New solutions to a number of nonlinear problems are presented, illustrating the originality of the HAM. Mathematica codes are freely available online to make it easy for readers to understand and use the HAM. This book is suitable for researchers and postgraduates in applied mathematics, physics, nonlinear mechanics, finance and engineering. Dr. Shijun Liao, a distinguished professor of Shanghai Jiao Tong University, is a pioneer of the HAM
Label
Homotopy analysis method in nonlinear differential equations, Shijun Liao
Instantiates
Publication
Antecedent source
unknown
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
  • Part II.
  • Mathematica Package BVPh and Its Applications
  • Mathematica Package BVPh
  • Nonlinear Boundary-value Problems with Multiple Solutions
  • Nonlinear Eigenvalue Equations with Varying Coefficients
  • A Boundary-layer Flow with an Infinite Number of Solutions
  • Non-similarity Boundary-layer Flows
  • Unsteady Boundary-layer Flows
  • Part III.
  • Applications in Nonlinear Partial Differential Equations
  • Part I.
  • Applications in Finance: American Put Options
  • Two and Three Dimensional Gelfand Equation
  • Interaction of Nonlinear Water Wave and Nonuniform Currents
  • Resonance of Arbitrary Number of Periodic Traveling Water Waves
  • Basic Ideas and Theorems
  • Introduction
  • Basic Ideas of the Homotopy Analysis Method
  • Optimal Homotopy Analysis Method
  • Systematic Descriptions and Related Theorems
  • Relationship to Euler Transform
  • Some Methods Based on the HAM
Control code
796995045
Dimensions
unknown
Extent
1 online resource (xiv, 565 pages)
File format
unknown
Form of item
online
Isbn
9787040322989
Level of compression
unknown
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other control number
9786613768537
Other physical details
illustrations (some color)
http://library.link/vocab/ext/overdrive/overdriveId
376853
Quality assurance targets
not applicable
Reformatting quality
unknown
Sound
unknown sound
Specific material designation
remote
System control number
(OCoLC)796995045
Label
Homotopy analysis method in nonlinear differential equations, Shijun Liao
Publication
Antecedent source
unknown
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
  • Part II.
  • Mathematica Package BVPh and Its Applications
  • Mathematica Package BVPh
  • Nonlinear Boundary-value Problems with Multiple Solutions
  • Nonlinear Eigenvalue Equations with Varying Coefficients
  • A Boundary-layer Flow with an Infinite Number of Solutions
  • Non-similarity Boundary-layer Flows
  • Unsteady Boundary-layer Flows
  • Part III.
  • Applications in Nonlinear Partial Differential Equations
  • Part I.
  • Applications in Finance: American Put Options
  • Two and Three Dimensional Gelfand Equation
  • Interaction of Nonlinear Water Wave and Nonuniform Currents
  • Resonance of Arbitrary Number of Periodic Traveling Water Waves
  • Basic Ideas and Theorems
  • Introduction
  • Basic Ideas of the Homotopy Analysis Method
  • Optimal Homotopy Analysis Method
  • Systematic Descriptions and Related Theorems
  • Relationship to Euler Transform
  • Some Methods Based on the HAM
Control code
796995045
Dimensions
unknown
Extent
1 online resource (xiv, 565 pages)
File format
unknown
Form of item
online
Isbn
9787040322989
Level of compression
unknown
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other control number
9786613768537
Other physical details
illustrations (some color)
http://library.link/vocab/ext/overdrive/overdriveId
376853
Quality assurance targets
not applicable
Reformatting quality
unknown
Sound
unknown sound
Specific material designation
remote
System control number
(OCoLC)796995045

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