Variational iteration technique for solving higher order boundary value problems

2007 ◽  
Vol 189 (2) ◽  
pp. 1929-1942 ◽  
Author(s):  
Muhammad Aslam Noor ◽  
Syed Tauseef Mohyud-Din
Keyword(s):  
Boundary Value Problems ◽  
Boundary Value ◽  
Higher Order ◽  
Variational Iteration ◽  
Iteration Technique

VARIATIONAL ITERATION METHOD FOR SOLVING NONLINEAR HIGHER-ORDER INITIAL AND BOUNDARY VALUE PROBLEMS

2009 ◽  
Vol 06 (04) ◽  
pp. 521-555 ◽  
Author(s):  
SYED TAUSEEF MOHYUD-DIN ◽  
MUHAMMAD ASLAM NOOR ◽  
KHALIDA INAYAT NOOR
Keyword(s):  
Boundary Value Problems ◽  
Iteration Method ◽  
Nonlinear Boundary ◽  
Iterative Scheme ◽  
Boundary Value ◽  
Variational Iteration Method ◽  
Higher Order ◽  
Nonlinear Boundary Value Problems ◽  
Variational Iteration ◽  
Adomian’S Polynomials

In this paper, we apply variational iteration method (VIM) and variational iteration method using Adomian's polynomials for solving nonlinear boundary value problems. The proposed iterative scheme finds the solution without any discretization, linearization, perturbation, or restrictive assumptions. Several examples are given to verify the accuracy and efficiency of the method. We have also considered an example where the proposed VIM is not reliable.

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 The Optimal Homotopy Asymptotic Method for the Solution of Higher-Order Boundary Value Problems in Finite Domains

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Javed Ali ◽  
S. Islam ◽  
Hamid Khan ◽  
Syed Inayat Ali Shah
Keyword(s):  
Boundary Value Problems ◽  
Asymptotic Method ◽  
Boundary Value ◽  
Nonlinear Problems ◽  
Higher Order ◽  
Variational Iteration ◽  
Homotopy Perturbation ◽  
Adomian Decomposition ◽  
Optimal Homotopy Asymptotic Method ◽  
Finite Domains

We solve some higher-order boundary value problems by the optimal homotopy asymptotic method (OHAM). The proposed method is capable to handle a wide variety of linear and nonlinear problems effectively. The numerical results given by OHAM are compared with the exact solutions and the solutions obtained by Adomian decomposition (ADM), variational iteration (VIM), homotopy perturbation (HPM), and variational iteration decomposition method (VIDM). The results show that the proposed method is more effective and reliable.

scholarly journals Existence and uniqueness criteria for the higher-order Hilfer fractional boundary value problems at resonance

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Yousef Gholami
Keyword(s):  
Boundary Value Problems ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Higher Order ◽  
Coupled Systems ◽  
At Resonance ◽  
Uniqueness Criteria ◽  
Fractional Boundary Value Problems

Abstract This investigation is devoted to the study of a certain class of coupled systems of higher-order Hilfer fractional boundary value problems at resonance. Combining the coincidence degree theory with the Lipschitz-type continuity conditions on nonlinearities, we present some existence and uniqueness criteria. Finally, to practically implement the obtained theoretical criteria, we give an illustrative application.

Sign in / Sign up

Export Citation Format

Share Document