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

2016 ◽  
Vol 2016 ◽  
pp. 1-14 ◽  
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.

scholarly journals Oscillation of first order linear differential equations with several non-monotone delays

2018 ◽  
Vol 16 (1) ◽  
pp. 83-94
Author(s):  
E.R. Attia ◽  
V. Benekas ◽  
H.A. El-Morshedy ◽  
I.P. Stavroulakis
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Linear Differential Equation ◽  
Linear Differential Equations ◽  
Order Linear Differential Equation ◽  
Order Linear ◽  
First Order ◽  
Linear Differential

AbstractConsider the first-order linear differential equation with several retarded arguments$$\begin{array}{} \displaystyle x^{\prime }(t)+\sum\limits_{k=1}^{n}p_{k}(t)x(\tau _{k}(t))=0,\;\;\;t\geq t_{0}, \end{array} $$where the functions pk, τk ∈ C([t0, ∞), ℝ+), τk(t) < t for t ≥ t0 and limt→∞τk(t) = ∞, for every k = 1, 2, …, n. Oscillation conditions which essentially improve known results in the literature are established. An example illustrating the results is given.

Oscillation of first-order differential equations with several non-monotone retarded arguments

2020 ◽  
Vol 27 (3) ◽  
pp. 341-350 ◽  
Author(s):  
Huseyin Bereketoglu ◽  
Fatma Karakoc ◽  
Gizem S. Oztepe ◽  
Ioannis P. Stavroulakis
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Linear Differential Equation ◽  
Order Linear Differential Equation ◽  
Oscillation Criteria ◽  
Order Linear ◽  
First Order ◽  
Linear Differential ◽  
First Order Differential Equations

AbstractConsider the first-order linear differential equation with several non-monotone retarded arguments {x^{\prime}(t)+\sum_{i=1}^{m}p_{i}(t)x(\tau_{i}(t))=0}, {t\geq t_{0}}, where the functions {p_{i},\tau_{i}\in C([t_{0},\infty),\mathbb{R}^{+})}, for every {i=1,2,\ldots,m}, {\tau_{i}(t)\leq t} for {t\geq t_{0}} and {\lim_{t\to\infty}\tau_{i}(t)=\infty}. New oscillation criteria which essentially improve the known results in the literature are established. An example illustrating the results is given.

scholarly journals Numerical Solution of First Order Linear Differential Equations in Fuzzy Environment by Modified Runge-Kutta- Method and Runga-Kutta-Merson-Method under generalized H-differentiability and its Application in Industry

2017 ◽  
Author(s):  
Sankar Prasad Mondal ◽  
Susmita Roy ◽  
Biswajit Das ◽  
Animesh Mahata
Keyword(s):  
Numerical Solution ◽  
Kutta Method ◽  
Order Linear ◽  
First Order ◽  
Generalized Hukuhara Derivative ◽  
Fuzzy Environment ◽  
Runge Kutta Method ◽  
Runge Kutta ◽  
Linear Differential ◽  
Fuzzy Solutions

The paper presents an adaptation of numerical solution of first order linear differential equation in fuzzy environment. The numerical method is re-established and studied with fuzzy concept to estimate its uncertain parameters whose values are not precisely known. Demonstrations of fuzzy solutions of the governing methods are carried out by the approaches, namely Modified Runge Kutta method and Runge Kutta Merson method. The results are compared with the exact solution which is found using generalized Hukuhara derivative (gH-derivative) concepts. Additionally, different illustrative examples and an application in industry of the methods are also undertaken with the useful table and graph to show the usefulness for attained to the proposed approaches.

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