Adomian Decomposition Method

The Adomian decomposition method (ADM) is an efficient semi‐analytical technique used for solving linear and nonlinear differential equations. It permits us to handle both nonlinear initial value problems (IVPs) and boundary value problems. The solution technique of this method is mainly...

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Published in:Advanced Numerical and Semi-Analytical Methods for Differential Equations pp. 119 - 130
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:
Adomian decomposition method
boundary value problems
linear differential equations
nonlinear differential equations
nonlinear initial value problems
ordinary differential equations
partial differential equations
semi‐analytical technique
Boundary value problems
IEEE Sections
Mathematical model
Ear
Convergence
ISBN:9781119423423, 1119423422
Online Access:Get full text
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Abstract The Adomian decomposition method (ADM) is an efficient semi‐analytical technique used for solving linear and nonlinear differential equations. It permits us to handle both nonlinear initial value problems (IVPs) and boundary value problems. The solution technique of this method is mainly based on decomposing the solution of nonlinear operator equation to a series of functions. Each presented term of the obtained series is developed from a polynomial generated in the expansion of an analytic function into a power series. This chapter presents procedures for solving linear as well as nonlinear ordinary/partial differential equations by the ADM along with example problems for clear understanding. It also presents linear and nonlinear IVPs for clear understanding of the ADM for ordinary differential equations. ADM transforms system of partial differential equations into a set of recursive relation that can easily be handled. To understand the method, one can consider the system of linear partial differential equations.
AbstractList The Adomian decomposition method (ADM) is an efficient semi‐analytical technique used for solving linear and nonlinear differential equations. It permits us to handle both nonlinear initial value problems (IVPs) and boundary value problems. The solution technique of this method is mainly based on decomposing the solution of nonlinear operator equation to a series of functions. Each presented term of the obtained series is developed from a polynomial generated in the expansion of an analytic function into a power series. This chapter presents procedures for solving linear as well as nonlinear ordinary/partial differential equations by the ADM along with example problems for clear understanding. It also presents linear and nonlinear IVPs for clear understanding of the ADM for ordinary differential equations. ADM transforms system of partial differential equations into a set of recursive relation that can easily be handled. To understand the method, one can consider the system of linear partial differential equations.
The Adomian decomposition method (ADM) is an efficient semi‐analytical technique used for solving linear and nonlinear differential equations. It permits us to handle both nonlinear initial value problems (IVPs) and boundary value problems. The solution technique of this method is mainly based on decomposing the solution of nonlinear operator equation to a series of functions. Each presented term of the obtained series is developed from a polynomial generated in the expansion of an analytic function into a power series. This chapter presents procedures for solving linear as well as nonlinear ordinary/partial differential equations by the ADM along with example problems for clear understanding. It also presents linear and nonlinear IVPs for clear understanding of the ADM for ordinary differential equations. ADM transforms system of partial differential equations into a set of recursive relation that can easily be handled. To understand the method, one can consider the system of linear partial differential equations.
Author Karunakar, Perumandla
Dilleswar Rao, Tharasi
Mahato, Nisha
Chakraverty, Snehashish
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Keywords Boundary value problems
IEEE Sections
Mathematical model
Ear
Convergence
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Batiha, Noorani, Hashim (c11-cit-0006) 2008; 1
Wazwaz (c11-cit-0001) 1998; 97
Adomian (c11-cit-0002) 1990; 13
Jafari, Daftardar‐Gejji (c11-cit-0005) 2006; 181
Bildik, Konuralp (c11-cit-0009) 2006; 7
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  year: 2009
  end-page: 2521
  ident: c11-cit-0007
  article-title: The solution of linear and nonlinear systems of Volterra functional equations using Adomian–Pade technique
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  article-title: Revised Adomian decomposition method for solving systems of ordinary and fractional differential equations
  publication-title: Applied Mathematics and Computation
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  ident: c11-cit-0009
  article-title: The use of variational iteration method, differential transform method and Adomian decomposition method for solving different types of nonlinear partial differential equations
  publication-title: International Journal of Nonlinear Sciences and Numerical Simulation
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  year: 1999
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  ident: c11-cit-0010
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Snippet The Adomian decomposition method (ADM) is an efficient semi‐analytical technique used for solving linear and nonlinear differential equations. It...
The Adomian decomposition method (ADM) is an efficient semi‐analytical technique used for solving linear and nonlinear differential equations. It permits us to...
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SubjectTerms Adomian decomposition method
boundary value problems
linear differential equations
nonlinear differential equations
nonlinear initial value problems
ordinary differential equations
partial differential equations
semi‐analytical technique
Title Adomian Decomposition Method
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