Numerical approximations for a class of nonlinear higher order singular boundary value problem by using homotopy perturbation and variational iteration method

2021 ◽  
Author(s):  
Biswajit Pandit ◽  
Amit Verma ◽  
Ravi P. Agarwal
Keyword(s):  
Boundary Value Problem ◽  
Iteration Method ◽  
Boundary Value ◽  
Variational Iteration Method ◽  
Higher Order ◽  
Singular Boundary ◽  
Singular Boundary Value Problem ◽  
Numerical Approximations ◽  
Variational Iteration ◽  
Homotopy Perturbation

scholarly journals Analytical solutions to contact problem with fractional derivatives in the sense of Caputo

2020 ◽  
Vol 24 (Suppl. 1) ◽  
pp. 313-323
Author(s):  
Muhammad Noor ◽  
Muhammad Rafiq ◽  
Salah-Ud-Din Khan ◽  
Muhammad Qureshi ◽  
Muhammad Kamran ◽  
...  
Keyword(s):  
Boundary Value Problem ◽  
Iteration Method ◽  
Boundary Value ◽  
Variational Iteration Method ◽  
Contact Problems ◽  
Function Technique ◽  
Fractional Boundary Value Problem ◽  
Variational Iteration ◽  
Residual Errors ◽  
Fractional Boundary Value Problems

The current study extends the applications of the variational iteration method for the analytical solution of fractional contact problems. The problem involves Caputo sense while calculating the derivative of fractional order, we apply the Penalty function technique to transform it into a system of fractional boundary value problems coupled with a known obstacle. The variational iteration method is employed to find the series solution of fractional boundary value problem. For different values of fractional parameters, residual errors of solutions are plotted to make sure the convergence and accuracy of the solution. The reasonably accurate results show that one of the highly effective and stable methods for the solution of fractional boundary value problem is the method of variational iteration.

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 Variational Iteration Method for Nonlinear Singular Two-Point Boundary Value Problems Arising in Human Physiology

2013 ◽  
Vol 2013 ◽  
pp. 1-4 ◽  
Author(s):  
Marwan Abukhaled
Keyword(s):  
Boundary Value Problems ◽  
Iteration Method ◽  
Boundary Value ◽  
Variational Iteration Method ◽  
Convergent Series ◽  
Singular Boundary ◽  
Singular Boundary Value Problems ◽  
Whittaker Functions ◽  
Exponential Integral ◽  
Variational Iteration

The variational iteration method is applied to solve a class of nonlinear singular boundary value problems that arise in physiology. The process of the method, which produces solutions in terms of convergent series, is explained. The Lagrange multipliers needed to construct the correctional functional are found in terms of the exponential integral and Whittaker functions. The method easily overcomes the obstacle of singularities. Examples will be presented to test the method and compare it to other existing methods in order to confirm fast convergence and significant accuracy.

scholarly journals Higher-Order Dynamic Delay Differential Equations on Time Scales

2012 ◽  
Vol 2012 ◽  
pp. 1-19
Author(s):  
Hua Su ◽  
Lishan Liu ◽  
Xinjun Wang
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Positive Solutions ◽  
Time Scales ◽  
Delay Differential Equations ◽  
Boundary Value ◽  
Higher Order ◽  
Singular Boundary ◽  
Singular Boundary Value Problem ◽  
Delay Differential

We study the existence of positive solutions for the nonlinear four-point singular boundary value problem with higher-orderp-Laplacian dynamic delay differential equations on time scales, subject to some boundary conditions. By using the fixed-point index theory, the existence of positive solution and many positive solutions for nonlinear four-point singular boundary value problem withp-Laplacian operator are obtained.

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

Sign in / Sign up

Export Citation Format

Share Document