Variational Iteration Method Solutions for Certain Thirteenth Order Ordinary Differential Equations

Abstract

In this paper, we extend variational iteration method (VIM) to find approximate solutions of linear and nonlinear thirteenth order differential equations in boundary value problems. The method is based on boundary valued problems. Two numerical examples are presented for the numerical illustration of the method and their results are compared with those considered by [1,2]. The results reveal that VIM is very effective and highly promising in comparison with other numerical methods.

Numerical Solutions of a Generalized Nth Order Boundary Value Problems Using Power Series Approximation Method

“…By increasing the order of approximation more accuracy can be obtained. Comparison of the results obtained with existing techniques [1] [2] shows that the PSAM is more efficient and accurate. Hence, it is easier and more economical to apply PSAM in solving BVPs.…”

“…Also, computational and rounding-off errors are avoided. The method has an excellent rate of convergence as compared with existing methods in [1] [2] and the exact solutions available in the literature. The rest of this paper will be organized as follows: Section 2 of this work give detailed Mathematical formulation of Nth order BVPs using PSAM.…”

“…Substituting (31) into Equation (7) for N = 0 (1) 11 we obtain ( ) The comparison of the approximate solution of example 1 obtained with the help of PSAM and the approximate solution using VIM obtained in [1] is given in Table 1. From the numerical results, it is clear that the PSAM is more efficient and accurate.…”

“…Over the years, several numerical techniques have been developed, such as the Variational Iteration Method (VIM) [1], Homotopy Perturbation Method (HPM) [2], Spline-Collocation Approximations Method (SCAM) [3], Spline Method [4], etc. that possess an elaborate procedure and structurally complex, which nevertheless yields efficient results.…”

Numerical solutions of higher order boundary value problems via wavelet approach

“…where Equation (33) represents 2M equations and 2M unknowns (wavelets coefficients). After calculating the unknowns, approximate solution can be obtained from Eq.…”