scholarly journals Sinc-Self-consistent method to solve a class of nonlinear eigenvalue differential equation

2021 ◽  
Author(s):  
Seyed Mohammad Ali Aleomraninejad ◽  
Mehdi Solaimani
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Subsequent Development ◽  
The Self ◽  
Infinite Domain ◽  
Numerical Examples ◽  
Smallest Eigenvalue ◽  
Sinc Methods ◽  
Self Consistent ◽  
Consistent Method

In this paper, we combine the sinc and self-consistent methods to solve a class of non-linear eigenvalue differential equations. Some properties of the self-consistent and sinc methods required for our subsequent development are given and employed. Numerical examples are included to demonstrate the validity and applicability of the introduced technique and a comparison is made with the existing results. The method is easy to implement and yields accurate results. We show that the sinc-self-consistent method can solve the equations on an infinite domain and produces the smallest eigenvalue with the most accuracy

scholarly journals A Novel Method for Solving Nonlinear Volterra Integro-Differential Equation Systems

2018 ◽  
Vol 2018 ◽  
pp. 1-6 ◽  
Author(s):  
Mohammad Hossein Daliri Birjandi ◽  
Jafar Saberi-Nadjafi ◽  
Asghar Ghorbani
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Exact Solutions ◽  
Iteration Method ◽  
Spectral Collocation ◽  
Numerical Examples ◽  
Integro Differential Equation ◽  
Collocation Technique ◽  
Computational Work ◽  
Novel Method

An efficient iteration method is introduced and used for solving a type of system of nonlinear Volterra integro-differential equations. The scheme is based on a combination of the spectral collocation technique and the parametric iteration method. This method is easy to implement and requires no tedious computational work. Some numerical examples are presented to show the validity and efficiency of the proposed method in comparison with the corresponding exact solutions.

Self-consistent estimates for the viscoelastic creep compliances of composite materials

1978 ◽  
Vol 359 (1697) ◽  
pp. 251-273 ◽  
Keyword(s):  
Composite Materials ◽  
Numerical Solutions ◽  
The Self ◽  
Inclusion Problem ◽  
Inclusion Problems ◽  
Viscoelastic Creep ◽  
Self Consistent ◽  
Title Problem ◽  
Consistent Method ◽  
Selection Of

In this paper the viscoelastic creep compliances of various composites are estimated by the self-consistent method. The phases may be arbitrarily anisotropic and in any concentrations but we demand that one of the phases be a matrix and the remaining phases consist of ellipsoidal inclusions. The theory is succinctly formulated with the help of Stieltjes convolutions. In order to solve the title problem, we first solve the misfitting viscoelastic inclusion problem. Numerical solutions are given for a selection of inclusion problems and for two common composite materials, namely an isotropic dispersion of spheres, and a uni-directional fibre reinforced material.

scholarly journals New Algorithm for the Numerical Solutions of Nonlinear Third-Order Differential Equations Using Jacobi-Gauss Collocation Method

2011 ◽  
Vol 2011 ◽  
pp. 1-14 ◽  
Author(s):  
A. H. Bhrawy ◽  
W. M. Abd-Elhameed
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Spectral Method ◽  
Collocation Method ◽  
Numerical Solutions ◽  
Order Differential Equation ◽  
Third Order ◽  
Numerical Examples ◽  
Collocation Spectral Method ◽  
Gauss Points

A new algorithm for solving the general nonlinear third-order differential equation is developed by means of a shifted Jacobi-Gauss collocation spectral method. The shifted Jacobi-Gauss points are used as collocation nodes. Numerical examples are included to demonstrate the validity and applicability of the proposed algorithm, and some comparisons are made with the existing results. The method is easy to implement and yields very accurate results.

Analysis of Mixed Mode Cracks in Two-Dimensional Magnetoelectroelastic Media

2006 ◽  
Vol 324-325 ◽  
pp. 403-406 ◽  
Author(s):  
Han Wang ◽  
Xian Hui Ke ◽  
Ming Hao Zhao
Keyword(s):  
Strain Energy Density ◽  
Mixed Mode ◽  
Strain Energy ◽  
The Self ◽  
Two Dimensional ◽  
Elliptical Cavity ◽  
Self Consistent ◽  
The Matrix ◽  
Consistent Method ◽  
Magnetoelectroelastic Medium

Based on the analytical solution for an elliptical cavity and the self-consistent method, the exact solutions for a crack in a two-dimensional magnetoelectroelastic medium is derived. The strain energy density factors are calculated for mixed mode cracks in a composite made of BaTiO3 as the inclusion and CoFe2O4 as the matrix.

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