Exponential function method for solving nonlinear ordinary differential equations with constant coefficients on a semi-infinite domain

2016 ◽  
Vol 126 (1) ◽  
pp. 79-97 ◽  
Author(s):  
EDMUND CHADWICK ◽  
ALI HATAM ◽  
SAEED KAZEM
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Exponential Function ◽  
Function Method ◽  
Nonlinear Ordinary Differential Equations ◽  
Infinite Domain ◽  
Constant Coefficients ◽  
Exponential Function Method

scholarly journals COMPARATIVE STUDY OF SOLUTION METHODS OF NON-HOMOGENEOUS LINEAR ORDINARY DIFFERENTIAL EQUATIONS WITH CONSTANT

2021 ◽  
Vol 16 (1) ◽  
Author(s):  
B Sivaram
Keyword(s):  
Differential Equations ◽  
Comparative Study ◽  
Ordinary Differential Equations ◽  
Exponential Function ◽  
Output Function ◽  
Linear Ordinary Differential Equations ◽  
Variation Of Parameters ◽  
Solution Methods ◽  
Constant Coefficients ◽  
Homogeneous Linear

The methods to obtain a solution of non-homogeneous linear ordinary differential equations with constant coefficients vary from type of output function. The present paper addresses the undetermined coefficients, variations of parameters methods and discussed the rewards and drawbacks of these methods with examples. The method of undetermined coefficients is derived from the variation of parameters when the out function is an exponential function.

scholarly journals On Adomian decomposition method for solving nonlinear ordinary differential equations of variable coefficients

2020 ◽  
Vol 4 (1) ◽  
pp. 476-484
Author(s):  
AbdulAzeez Kayode Jimoh ◽  
◽  
Aolat Olabisi Oyedeji ◽  
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Decomposition Method ◽  
Numerical Solutions ◽  
Adomian Decomposition Method ◽  
Variable Coefficients ◽  
Nonlinear Ordinary Differential Equations ◽  
Adomian Decomposition ◽  
Constant Coefficients ◽  
Derivatives Of

This paper considers the extension of the Adomian decomposition method (ADM) for solving nonlinear ordinary differential equations of constant coefficients to those equations with variable coefficients. The total derivatives of the nonlinear functions involved in the problem considered were derived in order to obtain the Adomian polynomials for the problems. Numerical experiments show that Adomian decomposition method can be extended as alternative way for finding numerical solutions to ordinary differential equations of variable coefficients. Furthermore, the method is easy with no assumption and it produces accurate results when compared with other methods in literature.

scholarly journals Impact of double-diffusive convection and motile gyrotactic microorganisms on magnetohydrodynamics bioconvection tangent hyperbolic nanofluid

Open Physics ◽  
2020 ◽  
Vol 18 (1) ◽  
pp. 74-88 ◽  
Author(s):  
Tanveer Sajid ◽  
Muhammad Sagheer ◽  
Shafqat Hussain ◽  
Faisal Shahzad
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Transfer Rate ◽  
Mass Transfer Rate ◽  
Physical Nature ◽  
Working Fluid ◽  
Nonlinear Ordinary Differential Equations ◽  
Gyrotactic Microorganisms ◽  
Motile Gyrotactic Microorganisms ◽  
Double Diffusive

AbstractThe double-diffusive tangent hyperbolic nanofluid containing motile gyrotactic microorganisms and magnetohydrodynamics past a stretching sheet is examined. By adopting the scaling group of transformation, the governing equations of motion are transformed into a system of nonlinear ordinary differential equations. The Keller box scheme, a finite difference method, has been employed for the solution of the nonlinear ordinary differential equations. The behaviour of the working fluid against various parameters of physical nature has been analyzed through graphs and tables. The behaviour of different physical quantities of interest such as heat transfer rate, density of the motile gyrotactic microorganisms and mass transfer rate is also discussed in the form of tables and graphs. It is found that the modified Dufour parameter has an increasing effect on the temperature profile. The solute profile is observed to decay as a result of an augmentation in the nanofluid Lewis number.

A Multiple Interval Chebyshev-Gauss-Lobatto Collocation Method for Ordinary Differential Equations

2016 ◽  
Vol 9 (4) ◽  
pp. 619-639 ◽  
Author(s):  
Zhong-Qing Wang ◽  
Jun Mu
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Collocation Method ◽  
Initial Value Problems ◽  
Numerical Experiments ◽  
High Order Accuracy ◽  
Nonlinear Ordinary Differential Equations ◽  
Initial Value ◽  
Order Accuracy ◽  
Long Time

AbstractWe introduce a multiple interval Chebyshev-Gauss-Lobatto spectral collocation method for the initial value problems of the nonlinear ordinary differential equations (ODES). This method is easy to implement and possesses the high order accuracy. In addition, it is very stable and suitable for long time calculations. We also obtain thehp-version bound on the numerical error of the multiple interval collocation method underH1-norm. Numerical experiments confirm the theoretical expectations.

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