Numerical solutions of linear and nonlinear Lane-Emden type equations by using magnus expansion method

2015 ◽  
Author(s):  
Cahit Köme ◽  
Mehmet Tarık Atay ◽  
Aytekin Eryilmaz ◽  
Sure Köme
Keyword(s):  
Numerical Solutions ◽  
Expansion Method ◽  
Magnus Expansion ◽  
Linear And Nonlinear

scholarly journals A Pseudospectral Algorithm for Solving Multipantograph Delay Systems on a Semi-Infinite Interval Using Legendre Rational Functions

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
E. H. Doha ◽  
D. Baleanu ◽  
A. H. Bhrawy ◽  
R. M. Hafez
Keyword(s):  
Numerical Solutions ◽  
Rational Functions ◽  
Absolute Error ◽  
Delay Systems ◽  
Infinite Interval ◽  
Algebraic Equations ◽  
Collocation Points ◽  
Nonlinear Algebraic Equations ◽  
Linear And Nonlinear ◽  
Pseudospectral Scheme

A new Legendre rational pseudospectral scheme is proposed and developed for solving numerically systems of linear and nonlinear multipantograph equations on a semi-infinite interval. A Legendre rational collocation method based on Legendre rational-Gauss quadrature points is utilized to reduce the solution of such systems to systems of linear and nonlinear algebraic equations. In addition, accurate approximations are achieved by selecting few Legendre rational-Gauss collocation points. The numerical results obtained by this method have been compared with various exact solutions in order to demonstrate the accuracy and efficiency of the proposed method. Indeed, for relatively limited nodes used, the absolute error in our numerical solutions is sufficiently small.

scholarly journals Modified Variational Iteration Algorithm-II: Convergence and Applications to Diffusion Models

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-14 ◽  
Author(s):  
Hijaz Ahmad ◽  
Tufail A. Khan ◽  
Predrag S. Stanimirović ◽  
Yu-Ming Chu ◽  
Imtiaz Ahmad
Keyword(s):  
Differential Equations ◽  
Numerical Solutions ◽  
Nonlinear Models ◽  
Nonlinear Differential Equations ◽  
Variational Iteration Method ◽  
Iteration Algorithm ◽  
Compact Finite Difference Method ◽  
Variational Iteration ◽  
Linear And Nonlinear ◽  
The Stability

Variational iteration method has been extensively employed to deal with linear and nonlinear differential equations of integer and fractional order. The key property of the technique is its ability and flexibility to investigate linear and nonlinear models conveniently and accurately. The current study presents an improved algorithm to the variational iteration algorithm-II (VIA-II) for the numerical treatment of diffusion as well as convection-diffusion equations. This newly introduced modification is termed as the modified variational iteration algorithm-II (MVIA-II). The convergence of the MVIA-II is studied in the case of solving nonlinear equations. The main advantage of the MVIA-II improvement is an auxiliary parameter which makes sure a fast convergence of the standard VIA-II iteration algorithm. In order to verify the stability, accuracy, and computational speed of the method, the obtained solutions are compared numerically and graphically with the exact ones as well as with the results obtained by the previously proposed compact finite difference method and second kind Chebyshev wavelets. The comparison revealed that the modified version yields accurate results, converges rapidly, and offers better robustness in comparison with other methods used in the literature. Moreover, the basic idea depicted in this study is relied upon the possibility of the MVIA-II being utilized to handle nonlinear differential equations that arise in different fields of physical and biological sciences. A strong motivation for such applications is the fact that any discretization, transformation, or any assumptions are not required for this proposed algorithm in finding appropriate numerical solutions.

A STUDY ABOUT THE SOLUTIONS OF SCHRÖDINGER EQUATION WITH AN ASYMPTOTICALLY LINEAR POTENTIAL

1996 ◽  
Vol 11 (03) ◽  
pp. 207-209 ◽  
Author(s):  
ELSO DRIGO FILHO
Keyword(s):  
Quantum Mechanics ◽  
Schrödinger Equation ◽  
Analytical Solutions ◽  
Schrodinger Equation ◽  
Numerical Solutions ◽  
Expansion Method ◽  
Linear Potential ◽  
Asymptotically Linear

We determine the solutions of the Schrödinger equation for an asymptotically linear potential. Analytical solutions are obtained by superalgebra in quantum mechanics and we establish when these solutions are possible. Numerical solutions for the spectra are obtained by the shifted 1/N expansion method.

scholarly journals A Note on Double Conformable Laplace Transform Method and Singular One Dimensional Conformable Pseudohyperbolic Equations

Mathematics ◽  
2019 ◽  
Vol 7 (10) ◽  
pp. 949 ◽  
Author(s):  
Hassan Eltayeb ◽  
Said Mesloub ◽  
Yahya T. Abdalla ◽  
Adem Kılıçman
Keyword(s):  
Present Method ◽  
Decomposition Method ◽  
Numerical Solutions ◽  
High Accuracy ◽  
Laplace Transform Method ◽  
Transform Method ◽  
Numerical Examples ◽  
One Dimensional ◽  
Linear And Nonlinear ◽  
Laplace Decomposition Method

The purpose of this article is to obtain the exact and approximate numerical solutions of linear and nonlinear singular conformable pseudohyperbolic equations and conformable coupled pseudohyperbolic equations through the conformable double Laplace decomposition method. Further, the numerical examples were provided in order to demonstrate the efficiency, high accuracy, and the simplicity of present method.

scholarly journals Vibration analysis of a mass on a spring by means of magnus expansion method

2016 ◽  
Vol 4 (2) ◽  
pp. 90-90
Author(s):  
Musa Basbuk ◽  
Aytekin Eryilmaz ◽  
Mehmet Tarik Atay
Keyword(s):  
Vibration Analysis ◽  
Expansion Method ◽  
Magnus Expansion

Assessment of Solutions to Vibration Problems Involving Piecewise Constant Exertions

2000 ◽  
Author(s):  
L. Dai
Keyword(s):  
Nonlinear Vibration ◽  
Existence And Uniqueness ◽  
Numerical Solutions ◽  
Numerical Calculations ◽  
Piecewise Constant ◽  
Truncation Errors ◽  
Piecewise Constant Argument ◽  
Vibration Problems ◽  
Linear And Nonlinear ◽  
Constant Argument

Abstract Direct analytical and numerical solutions are constructed for linear and nonlinear vibration problems involving piecewise constant exertions. Existence and uniqueness of the solutions and the truncation errors of the numerical calculations are also analysed. With the employment of a piecewise constant argument, vibration systems with piecewise constant exertions are connected with the corresponding systems with continuous exertions.

scholarly journals The Approximate Solutions of Fredholm Integrodifferential-Difference Equations with Variable Coefficients via Homotopy Analysis Method

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Seydi Battal Gazi Karakoç ◽  
Aytekin Eryılmaz ◽  
Musa Başbük
Keyword(s):  
Difference Equations ◽  
Homotopy Analysis Method ◽  
Algebraic System ◽  
Numerical Solutions ◽  
Numerical Procedure ◽  
Approximate Solutions ◽  
Variable Coefficients ◽  
Analysis Method ◽  
Homotopy Analysis ◽  
Linear And Nonlinear

Numerical solutions of linear and nonlinear integrodifferential-difference equations are presented using homotopy analysis method. The aim of the paper is to present an efficient numerical procedure for solving linear and nonlinear integrodifferential-difference equations. The reliability and efficiency of the proposed scheme are demonstrated by some numerical experiments and performed on the computer algebraic system.

scholarly journals Numerical Simulations for Solving Fuzzy Fractional Differential Equations by Max-Min Improved Euler Methods

2015 ◽  
Vol 7 (1) ◽  
pp. 53-83 ◽  
Author(s):  
Najeeb Alam Khan ◽  
Oyoon Abdul Razzaq ◽  
Fatima Riaz
Keyword(s):  
Differential Equations ◽  
Numerical Simulations ◽  
Fractional Differential Equations ◽  
Initial Value Problems ◽  
Numerical Solutions ◽  
Initial Value ◽  
Fractional Differential ◽  
Linear And Nonlinear ◽  
Euler Methods ◽  
Fuzzy Fractional Differential Equations

Abstract In this paper, an extension is introduced into Max-Min Improved Euler methods for solving initial value problems of fuzzy fractional differential equations (FFDEs). Two modified fractional Euler type methods have been proposed and investigated to obtain numerical solutions of linear and nonlinear FFDEs. The proposed algorithms are tested on various illustrative examples. Exact values are also simulated to compare and discuss the closeness and accuracy of approximations so obtained. Comparatively, tables and graphs results reveal the complete reliability, efficiency and accuracy of the proposed methods.

Sign in / Sign up

Export Citation Format

Share Document