Comments on two papers dealing with approximate solutions to non-linear differential equations

1974 ◽  
Vol 19 (3) ◽  
pp. 661-662 ◽  
Author(s):  
A. C. SOUDACK
Keyword(s):  
Differential Equations ◽  
Approximate Solutions ◽  
Linear Differential Equations ◽  
Non Linear ◽  
Linear Differential

scholarly journals On non-homogeneous canonical third-order linear differential equations

1994 ◽  
Vol 57 (2) ◽  
pp. 138-148 ◽  
Author(s):  
N. Parhi
Keyword(s):  
Differential Equations ◽  
Linear Equations ◽  
Sufficient Conditions ◽  
Linear Differential Equations ◽  
Third Order ◽  
Order Linear ◽  
Non Linear ◽  
Linear Differential ◽  
Non Linear Equations

AbstractIn this paper sufficient conditions have been obtained for non-oscillation of non-homogeneous canonical linear differential equations of third order. Some of these results have been extended to non-linear equations.

scholarly journals Pendulum with aerodynamic and viscous damping

2020 ◽  
Vol 3 (2) ◽  
pp. 43-47
Author(s):  
Herlin Soraya
Keyword(s):  
Differential Equations ◽  
Stable State ◽  
The State ◽  
Linear Differential Equations ◽  
Viscous Damping ◽  
Viscous Damper ◽  
Aerodynamic Damping ◽  
Non Linear ◽  
Linear Differential ◽  
The Relationship

In this paper we discuss about how the relationship between non-linear differential equations on aerodynamic damping with linearly viscous damping equations. And it turns out after analyzing that the changes that occur pendulum that changes from the start of the maximum state to a stable state takes time so that changes that occur until the state is stable, this change can be reduced with the use of viscous damper

scholarly journals Boundedness of Solutions for Second Order Differential Equations

2020 ◽  
Vol 12 (4) ◽  
pp. 58
Author(s):  
Daniel C. Biles
Keyword(s):  
Differential Equations ◽  
Sufficient Conditions ◽  
Second Order ◽  
Linear Differential Equations ◽  
Boundedness Of Solutions ◽  
Second Order Differential Equations ◽  
All Solutions ◽  
Non Linear ◽  
Linear Differential

We present new theorems which specify sufficient conditions for the boundedness of all solutions for second order non-linear differential equations. Unboundedness of solutions is also considered.

scholarly journals Modelling of a non-linear coil with loss in iron using the Runge-Kutta methods

2016 ◽  
Vol 65 (3) ◽  
pp. 527-539 ◽  
Author(s):  
Joanna Kolańska-Płuska ◽  
Barbara Grochowicz
Keyword(s):  
Differential Equations ◽  
State Space ◽  
Linear Differential Equations ◽  
Non Linear ◽  
Runge Kutta ◽  
Linear Differential ◽  
Space Description

Abstract This work presents a study on dynamics of a circuit with a non-linear coil, where loss in iron is also taken into account. A coil model is derived using a state space description. The work also includes the development of an application in C# for coil dynamics examination, where the implicit RADAU IIA method of various orders is applied for the purpose of solving non-linear differential equations modelling the non-linear coil with loss in iron.

scholarly journals On a class of non-linear differential equations with exact solution

2012 ◽  
Vol 34 (1) ◽  
pp. 7-17
Author(s):  
Dao Huy Bich ◽  
Nguyen Dang Bich
Keyword(s):  
Exact Solution ◽  
Differential Equations ◽  
Exact Solutions ◽  
Solid Mechanics ◽  
Linear Equations ◽  
Linear Differential Equations ◽  
Second Order Differential Equations ◽  
Non Linear ◽  
Linear Differential ◽  
Non Linear Equations

The present paper deals with a class of non-linear ordinary second-order differential equations with exact solutions. A procedure for finding the general exact solution based on a known particular one is derived. For illustration solutions of some non-linear equations occurred in many problems of solid mechanics are considered.

scholarly journals A computational method for solving differential equations with quadratic nonlinearity by using Bernoulli polynomials

2019 ◽  
Vol 23 (Suppl. 1) ◽  
pp. 275-283
Author(s):  
Kubra Bicer ◽  
Mehmet Sezer
Keyword(s):  
Differential Equations ◽  
Linear Equations ◽  
Bernoulli Polynomials ◽  
Approximate Solutions ◽  
Mean Value ◽  
Computational Method ◽  
Mean Value Theorem ◽  
Residual Functions ◽  
Non Linear ◽  
Linear Differential

In this paper, a matrix method is developed to solve quadratic non-linear differential equations. It is assumed that the approximate solutions of main problem which we handle primarily, is in terms of Bernoulli polynomials. Both the approximate solution and the main problem are written in matrix form to obtain the solution. The absolute errors are applied to numeric examples to demonstrate efficiency and accuracy of this technique. The obtained tables and figures in the numeric examples show that this method is very sufficient and reliable for solution of non-linear equations. Also, a formula is utilized based on residual functions and mean value theorem to seek error bounds.

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