Solution of first order system of differential equation in fuzzy environment and its application

The work presented here analyses the structural corrosion degradation of two sets of corrosion depth measurements collected with a one-decade difference. The corrosion degradation process is associated to a first order system, subjected to a sudden disturbance, where a step function is used as an input to define the solution of the differential equation of this system leads to the exponential corrosion degradation model as developed earlier. Corrosion margins of redundant ship structures with serious consequences of failure are derived and several conclusions related to the new trend in the ageing structures are presented and discussed. Partial safety factors with respect to the corrosion environment and corrosion margins are developed that can be used in the design, avoiding a complex probabilistic analysis.

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Asymptotic Solutions of a 6th Order Differential Equation with Two Turning Points. Part II: Derivation by Reduction to a First Order System

SIAM Journal on Mathematical Analysis ◽

10.1137/0503012 ◽

1972 ◽

Vol 3 (1) ◽

pp. 93-104 ◽

Cited By ~ 1

Author(s):

B. Granoff

Keyword(s):

Differential Equation ◽

Order Differential Equation ◽

Turning Points ◽

Asymptotic Solutions ◽

Order System ◽

First Order

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

Journal of Uncertainty in Mathematics Science ◽

10.5899/2014/jums-00008 ◽

2014 ◽

Vol 2014 ◽

pp. 1-18

Author(s):

Sankar Prasad Mondal ◽

Tapan Kumar Roy

Keyword(s):

Differential Equation ◽

Ordinary Differential Equation ◽

Lagrange Multiplier ◽

Lagrange Multiplier Method ◽

Multiplier Method ◽

Order Linear ◽

First Order ◽

Fuzzy Environment

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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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A General Approximate Solution for Stretching Problems in Viscous Fluid

Zeitschrift für Naturforschung A ◽

10.1515/zna-2015-0047 ◽

2015 ◽

Vol 70 (9) ◽

pp. 781-786

Author(s):

Saleem Asghar ◽

Mudassar Jalil ◽

Ahmed Alsaedi

Keyword(s):

Differential Equation ◽

Approximate Solution ◽

Boundary Value Problem ◽

Analytic Solution ◽

Boundary Value ◽

Skin Friction Coefficient ◽

Order System ◽

First Order ◽

Exponential Stretching ◽

Special Cases

AbstractIn this study, we propose a boundary value problem that contains two arbitrary parameters in the differential equation and show that the results of a number of existing stretching problems (linear, power law, and exponential stretching) are the special cases of the proposed boundary value problem. A two-term analytic asymptotic solution of this problem is developed by introducing a small parameter in the differential equation. Interest lies in the finding of rare exact analytical solutions for the zeroth and first order systems. Surprisingly, only a two-term closed form of analytical solution shows an excellent match with the existing literature. The solution for second-order system is found numerically to improve the accuracy of the approximate solution. The generalised analytic solution is tested over a number of stretching problems for the velocity field and skin friction coefficient showing an excellent match. In conclusion, various stretching problems discussed in literature are special cases of this study.

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Gradient Structures Associated with a Polynomial Differential Equation

Mathematics ◽

10.3390/math8040535 ◽

2020 ◽

Vol 8 (4) ◽

pp. 535 ◽

Cited By ~ 3

Author(s):

Savin Treanţă

Keyword(s):

Differential Equation ◽

Order System ◽

Mathematical Framework ◽

Special Significance ◽

First Order ◽

System Method ◽

Polynomial Differential Equation ◽

The Cauchy Problem ◽

Finite Set ◽

Kernel Representation

In this paper, by using the characteristic system method, the kernel of a polynomial differential equation involving a derivation in R n is described by solving the Cauchy Problem for the corresponding first order system of PDEs. Moreover, the kernel representation has a special significance on the space of solutions to the corresponding system of PDEs. As very important applications, it has been established that the mathematical framework developed in this work can be used for the study of some second-order PDEs involving a finite set of derivations.

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