Adomian Decomposition Method for Computing Eigen-Values of Singular Sturm–Liouville Problems

Singh, Neelima; Kumar, Manoj

doi:10.1007/s40009-013-0127-1

Cited by 4 publications

(1 citation statement)

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“…Some examples will be given to illustrate the idea. For more details on using Adomian's techniques in finding eigenvalues see [27].…”

Section: Adomian-variational Iteration Method(avim)mentioning

confidence: 99%

Comparison Methods for Solving Non-Linear Sturm–Liouville Eigenvalues Problems

Al‐Khaled¹,

Hazaimeh²

2020

Symmetry

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In this paper, we present a comparative study between Sinc–Galerkin method and a modified version of the variational iteration method (VIM) to solve non-linear Sturm–Liouville eigenvalue problem. In the Sinc method, the problem under consideration was converted from a non-linear differential equation to a non-linear system of equations, that we were able to solve it via the use of some iterative techniques, like Newton’s method. The other method under consideration is the VIM, where the VIM has been modified through the use of the Laplace transform, and another effective modification has also been made to the VIM by replacing the non-linear term in the integral equation resulting from the use of the well-known VIM with the Adomian’s polynomials. In order to explain the advantages of each method over the other, several issues have been studied, including one that has an application in the field of spectral theory. The results in solutions to these problems, which were included in tables, showed that the improved VIM is better than the Sinc method, while the Sinc method addresses some advantages over the VIM when dealing with singular problems.

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“…Some examples will be given to illustrate the idea. For more details on using Adomian's techniques in finding eigenvalues see [27].…”

Section: Adomian-variational Iteration Method(avim)mentioning

confidence: 99%