Solution of First Order Linear Non Homogeneous Ordinary Differential Equation in Fuzzy Environment Based on Lagrange Multiplier Method

SynopsisBy use of the theory of asymptotic expansions for first-order linear systems of ordinary differential equations, asymptotic formulas are obtained for the solutions of annth order linear homogeneous ordinary differential equation with complex coefficients having asymptotic expansions in a sector of the complex plane. These asymptotic formulas involve the roots of certain polynomials whose coefficients are obtained from the asymptotic expansions of the coefficients of the differential operator.

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Numerical Solution of First-Order Linear Differential Equations in Fuzzy Environment by Runge-Kutta-Fehlberg Method and Its Application

International Journal of Differential Equations ◽

10.1155/2016/8150497 ◽

2016 ◽

Vol 2016 ◽

pp. 1-14 ◽

Cited By ~ 2

Author(s):

Sankar Prasad Mondal ◽

Susmita Roy ◽

Biswajit Das

Keyword(s):

Differential Equation ◽

Error Analysis ◽

Exact Solutions ◽

Numerical Solutions ◽

Order Linear Differential Equation ◽

Order Linear ◽

First Order ◽

Fuzzy Environment ◽

Runge Kutta ◽

Linear Differential

The numerical algorithm for solving “first-order linear differential equation in fuzzy environment” is discussed. A scheme, namely, “Runge-Kutta-Fehlberg method,” is described in detail for solving the said differential equation. The numerical solutions are compared with (i)-gH and (ii)-gH differential (exact solutions concepts) system. The method is also followed by complete error analysis. The method is illustrated by solving an example and an application.

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STRONGLY IRREGULAR PERIODIC SOLUTIONS OF THE FIRST-ORDER LINEAR HOMOGENEOUS DISCRETE EQUATION

Doklady of the National Academy of Sciences of Belarus ◽

10.29235/1561-8323-2018-62-3-263-267 ◽

2018 ◽

Vol 62 (3) ◽

pp. 263-267 ◽

Cited By ~ 1

Author(s):

A. K. Demenchuk

Keyword(s):

Differential Equation ◽

Ordinary Differential Equation ◽

Periodic Solutions ◽

Difference Equations ◽

Prime Numbers ◽

Discrete Equation ◽

Linear Difference Equations ◽

Order Linear ◽

First Order ◽

Discrete Equations

In 1950 J. Massera proved that a fi rst-order scalar periodic ordinary differential equation has no strongly ira proved that a first-order scalar periodic ordinary differential equation has no strongly irregular periodic solutions, that is, such solutions whose period of solution is incommensurable with the period of equation. For difference equations with discrete time, strong irregularity means that the period of the equation and the period of its solution are relatively prime numbers. It is known that in the case of discrete equations, the above result of J. Massera has no complete analog.The purpose of this article is to investigate the possibility to realize Massera’s theorem for certain classes of difference equations. To do this, we consider the class of linear difference equations. It is proved that a first-order linear homogeneous non-stationary periodic discrete equation has no strongly irregular non-stationary periodic solutions.

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