Approximate solution of Lane-Emden problem via modified Hermite operation matrix method

2021 ◽  
Vol 2 (2) ◽  
pp. 57-67
Author(s):  
Bushra Esaa Kashem ◽  
Suha SHIHAB
Keyword(s):  
Approximate Solution ◽  
Initial Value Problems ◽  
Operational Matrix ◽  
Mathematical Physics ◽  
Initial Value ◽  
Solution Function ◽  
Emden Equation ◽  
Physical Problems ◽  
Operational Matrix Of Integration ◽  
The Given

Lane-Emden equations are singular initial value problems and they are important in mathematical physics and astrophysics. The aim of this present paper is presenting a new numerical method for finding approximate solution to Lane-Emden type equations arising in astrophysics based on modified Hermite operational matrix of integration. The proposed technique is based on taking the truncated modified Hermite series of the solution function in the Lane-Emden equation and then transferred into a matrix equation together with the given conditions. The obtained result is system of linear algebraic equation using collection points. The suggested algorithm is applied on some relevant physical problems as Lane-Emden type equations.

scholarly journals Modified Hermite Operational Matrix Method for Nonlinear Lane-Emden Problem

2020 ◽  
Vol 25 (3) ◽  
pp. 71-79
Author(s):  
Bushra Eesa
Keyword(s):  
Nonlinear System ◽  
Present Method ◽  
Operational Matrix ◽  
Mathematical Physics ◽  
Solution Function ◽  
Emden Equation ◽  
Operational Matrix Method ◽  
Physical Problems ◽  
The Given ◽  
Hermite Series

Nonlinear Lane –Emden equations are significant in astrophysics and mathematical physics. The aim of this paper is submitted a new approximate method for finding solution to nonlinear Lane-Emden type equations appearing in astrophysics based on modified Hermite integration operational matrix. The suggest technique is based on taking the truncated modified Hermite series of the solution function in the nonlinear Lane-Emden equation and then changed into a matrix equation with the given conditions. Nonlinear system of algebraic equation using collection points is obtained. The present method is applied on some relevant physical problems as nonlinear Lane-Emden type equations.

scholarly journals Variational Iteration Method for Analytical Solution of the Lane-Emden Type Equation with Singular Initial and Boundary Conditions

2019 ◽  
pp. 127-142 ◽  
Author(s):  
Muhammad Nadeem ◽  
Hijaz Ahmad
Keyword(s):  
Exact Solution ◽  
Analytical Solution ◽  
Iteration Method ◽  
Initial Value Problems ◽  
Type Equation ◽  
Variational Iteration Method ◽  
Mathematical Physics ◽  
Initial Value ◽  
Emden Equation ◽  
Variational Iteration

In this paper, a well-known equation used in astrophysics and mathematical physics called the Lane-Emden equation is to be solved by a variational iteration method. The main purpose of this approach is to solve the singular initial value problems and also boundary value problem of Lane-Emden type equations. This technique overcomes its singularity at origin rapidly. It gives the approximate and exact solution with easily computable terms. The approach is illustrated with some examples to show its reliability and compactness.

scholarly journals New Analytic Solution to the Lane-Emden Equation of Index 2

2012 ◽  
Vol 2012 ◽  
pp. 1-19 ◽  
Author(s):  
S. S. Motsa ◽  
S. Shateyi
Keyword(s):  
Analytical Methods ◽  
Initial Value Problems ◽  
Analytic Solution ◽  
Mathematical Physics ◽  
Numerical Results ◽  
Initial Value ◽  
Emden Equation ◽  
New Methods ◽  
Index 2 ◽  
Good Agreement

We present two new analytic methods that are used for solving initial value problems that model polytropic and stellar structures in astrophysics and mathematical physics. The applicability, effectiveness, and reliability of the methods are assessed on the Lane-Emden equation which is described by a second-order nonlinear differential equation. The results obtained in this work are also compared with numerical results of Horedt (1986) which are widely used as a benchmark for testing new methods of solution. Good agreement is observed between the present results and the numerical results. Comparison is also made between the proposed new methods and existing analytical methods and it is found that the new methods are more efficient and have several advantages over some of the existing analytical methods.

scholarly journals Approximate solution of nonlinear ordinary differential equation using ZZ decomposition method

2020 ◽  
Vol 4 (1) ◽  
pp. 448-455
Author(s):  
Mulugeta Andualem ◽  
◽  
Atinafu Asfaw ◽  
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Approximate Solution ◽  
Initial Value Problems ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Nonlinear Ordinary Differential Equation ◽  
Initial Value ◽  
Transform Method ◽  
Adomian Decomposition

Nonlinear initial value problems are somewhat difficult to solve analytically as well as numerically related to linear initial value problems as their variety of natures. Because of this, so many scientists still searching for new methods to solve such nonlinear initial value problems. However there are many methods to solve it. In this article we have discussed about the approximate solution of nonlinear first order ordinary differential equation using ZZ decomposition method. This method is a combination of the natural transform method and Adomian decomposition method.

scholarly journals Approximate Solution of Linear Fuzzy Initial Value Problems Using Modified Variaional Iteration Method

2021 ◽  
Vol 24 (4) ◽  
pp. 32-39
Author(s):  
Hussein M. Sagban ◽  
◽  
Fadhel S. Fadhel ◽  
Keyword(s):  
Approximate Solution ◽  
Rate Of Convergence ◽  
Initial Value Problem ◽  
Iteration Method ◽  
Initial Value Problems ◽  
Initial Conditions ◽  
Variational Iteration Method ◽  
Initial Value ◽  
Variational Iteration ◽  
Modified Variational Iteration Method

The main objective of this paper is to solve fuzzy initial value problems, in which the fuzziness occurs in the initial conditions. The proposed approach, namely the modified variational iteration method, will be used to find the solution of fuzzy initial value problem approximately and to increase the rate of convergence of the variational iteration method. From the obtained results, as it is expected, the approximate results of the proposed method are more accurate than those results obtained without using the modified variational iteration method.

scholarly journals A numerical study for inward solidification of a liquid contained in cylindrical and spherical vessel

2010 ◽  
Vol 14 (2) ◽  
pp. 365-372 ◽  
Author(s):  
Kirby Rajeev ◽  
Subir Das
Keyword(s):  
Numerical Study ◽  
Operational Matrix ◽  
Interface Condition ◽  
Initial Value ◽  
Spherical Vessel ◽  
Interface Position ◽  
Operational Matrix Of Integration ◽  
Fixed Interface ◽  
Vector Matrix ◽  
Change Material

This study presents a numerical solution of inward solidification of phase change material contained in cylinder/sphere. Here, constant thermal property is assumed throughout the analysis for the liquid, which is initially at fusion temperature. The governing dimensionless equations of the above problem and boundary conditions are converted to initial value problem of vector matrix form. The time function is approximated by Chebyshev series and the operational matrix of integration is applied. The solution is utilized iteratively in the interface condition to determine the time taken to attain a fixed interface position.

scholarly journals An Optimized 5-Point Block Formula for Direct Numerical Solution of First Order Stiff Initial Value Problems

2020 ◽  
Vol 3 (2) ◽  
pp. 158-167
Author(s):  
VO Atabo ◽  
PO Olatunji
Keyword(s):  
Approximate Solution ◽  
Test Performance ◽  
Initial Value Problems ◽  
Power Series Expansion ◽  
Initial Value ◽  
First Order ◽  
Research Article ◽  
Error Constant ◽  
Direct Numerical Solution ◽  
Collocation Approach

In this research article, we focus on the formulation of a 5-point block formula for solving first order ordinary differential equations (ODEs). The method is formulated via interpolation and collocation approach using power series expansion as the approximate solution. It has been established that the derived method is of order six. Basic properties such zero and absolute stabilities, convergence, order and error constant have also been investigated. The accuracy of the method was verified on some selected stiff IVPs, compared with some existing methods (DIBBDF, SDIBBDF, BBDF(4), BBDF(5) and odes15s) and test performance showed that the new method is viable.

Sign in / Sign up

Export Citation Format

Share Document