scholarly journals Approximate solutions to boundary value problems of higher order by the modified decomposition method

2000 ◽  
Vol 40 (6-7) ◽  
pp. 679-691 ◽  
Author(s):  
A.-M. Wazwaz
Keyword(s):  
Boundary Value Problems ◽  
Decomposition Method ◽  
Boundary Value ◽  
Approximate Solutions ◽  
Higher Order

scholarly journals Numerical Solution of Higher Order Boundary Value Problems

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Shahid S. Siddiqi ◽  
Muzammal Iftikhar
Keyword(s):  
Boundary Value Problems ◽  
Homotopy Analysis Method ◽  
Present Method ◽  
Boundary Value ◽  
Approximate Solutions ◽  
Convergent Series ◽  
Higher Order ◽  
Analysis Method ◽  
Homotopy Analysis ◽  
Linear And Nonlinear

The aim of this paper is to use the homotopy analysis method (HAM), an approximating technique for solving linear and nonlinear higher order boundary value problems. Using HAM, approximate solutions of seventh-, eighth-, and tenth-order boundary value problems are developed. This approach provides the solution in terms of a convergent series. Approximate results are given for several examples to illustrate the implementation and accuracy of the method. The results obtained from this method are compared with the exact solutions and other methods (Akram and Rehman (2013), Farajeyan and Maleki (2012), Geng and Li (2009), Golbabai and Javidi (2007), He (2007), Inc and Evans (2004), Lamnii et al. (2008), Siddiqi and Akram (2007), Siddiqi et al. (2012), Siddiqi et al. (2009), Siddiqi and Iftikhar (2013), Siddiqi and Twizell (1996), Siddiqi and Twizell (1998), Torvattanabun and Koonprasert (2010), and Kasi Viswanadham and Raju (2012)) revealing that the present method is more accurate.

scholarly journals A Modified Adomian Decomposition Method for Solving Higher-Order Singular Boundary Value Problems

2010 ◽  
Vol 65 (12) ◽  
pp. 1093-1100 ◽  
Author(s):  
Weonbae Kim ◽  
Changbum Chun
Keyword(s):  
Boundary Value Problems ◽  
Decomposition Method ◽  
Boundary Value ◽  
Adomian Decomposition Method ◽  
Higher Order ◽  
Singular Boundary ◽  
Singular Boundary Value Problems ◽  
Adomian Polynomials ◽  
Modified Adomian Decomposition Method ◽  
Adomian Decomposition

In this paper, we present a reliable modification of the Adomian decomposition method for solving higher-order singular boundary value problems. He’s polynomials are also used to overcome the complex and difficult calculation of Adomian polynomials occurring in the application of the Adomian decomposition method. Numerical examples are given to illustrate the accuracy and efficiency of the presented method, revealing its reliability and applicability in handling the problems with singular nature.

scholarly journals On the Solutions of Nonlinear Higher-Order Boundary Value Problems by Using Differential Transformation Method and Adomian Decomposition Method

2011 ◽  
Vol 2011 ◽  
pp. 1-19 ◽  
Author(s):  
Che Haziqah Che Hussin ◽  
Adem Kiliçman
Keyword(s):  
Boundary Value Problems ◽  
Decomposition Method ◽  
Nonlinear Differential Equations ◽  
Boundary Value ◽  
Adomian Decomposition Method ◽  
Transformation Method ◽  
Higher Order ◽  
Differential Transformation Method ◽  
Differential Transformation ◽  
Adomian Decomposition

We study higher-order boundary value problems (HOBVP) for higher-order nonlinear differential equation. We make comparison among differential transformation method (DTM), Adomian decomposition method (ADM), and exact solutions. We provide several examples in order to compare our results. We extend and prove a theorem for nonlinear differential equations by using the DTM. The numerical examples show that the DTM is a good method compared to the ADM since it is effective, uses less time in computation, easy to implement and achieve high accuracy. In addition, DTM has many advantages compared to ADM since the calculation of Adomian polynomial is tedious. From the numerical results, DTM is suitable to apply for nonlinear problems.

scholarly journals Analytical approximate solution of higher order boundary value problems via variational iteration method

BIBECHANA ◽  
2017 ◽  
Vol 15 ◽  
pp. 37-42
Author(s):  
Jamshad Ahmad ◽  
Zobia Hamid
Keyword(s):  
Approximate Solution ◽  
Mathematical Models ◽  
Boundary Value Problems ◽  
Iteration Method ◽  
Boundary Value ◽  
Variational Iteration Method ◽  
Approximate Solutions ◽  
Higher Order ◽  
Analytical Approximate Solution ◽  
Variational Iteration

In this paper, application of variational iteration method has been successfully extended to obtain approximate solutions of some higher order boundary value problems. We emphasize the power of the method by testing three different mathematical models of distinct orders. The results are obtained by using only little iteration.  BIBECHANA 15 (2018) 37-42

scholarly journals An Efficient Higher-Order Quasilinearization Method for Solving Nonlinear BVPs

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Eman S. Alaidarous ◽  
Malik Zaka Ullah ◽  
Fayyaz Ahmad ◽  
A.S. Al-Fhaid
Keyword(s):  
Boundary Value Problems ◽  
Decomposition Method ◽  
Order Of Convergence ◽  
Nonlinear Differential Equations ◽  
Boundary Value ◽  
Higher Order ◽  
Critical Parameters ◽  
Computational Performance ◽  
Highly Nonlinear ◽  
Quasilinearization Methods

In this research paper, we present higher-order quasilinearization methods for the boundary value problems as well as coupled boundary value problems. The construction of higher-order convergent methods depends on a decomposition method which is different from Adomain decomposition method (Motsa and Sibanda, 2013). The reported method is very general and can be extended to desired order of convergence for highly nonlinear differential equations and also computationally superior to proposed iterative method based on Adomain decomposition because our proposed iterative scheme avoids the calculations of Adomain polynomials and achieves the same computational order of convergence as authors have claimed in Motsa and Sibanda, 2013. In order to check the validity and computational performance, the constructed iterative schemes are also successfully applied to bifurcation problems to calculate the values of critical parameters. The numerical performance is also tested for one-dimension Bratu and Frank-Kamenetzkii equations.

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