scholarly journals On new solutions of linear system of first -order fuzzy differential equations with fuzzy coefficient

2016 ◽  
Vol 2016 ◽  
pp. 110-117 ◽  
Author(s):  
A. Karimi Dizicheh ◽  
S. Salahshour ◽  
F. Ismail ◽  
A. Ahmadian Hosseini
Keyword(s):  
Linear System ◽  
Differential Equations ◽  
First Order

scholarly journals A parameter uniform almost first order convergent numerical method for non-linear system of singularly perturbed differential equations

BIOMATH ◽  
2016 ◽  
Vol 5 (2) ◽  
pp. 1608111
Author(s):  
Ishwariya Raj ◽  
Princy Mercy Johnson ◽  
John J.H Miller ◽  
Valarmathi Sigamani
Keyword(s):  
Linear System ◽  
Differential Equations ◽  
Numerical Method ◽  
Shishkin Mesh ◽  
Singularly Perturbed ◽  
Initial Value ◽  
First Order ◽  
Non Linear ◽  
Perturbation Parameters ◽  
Non Linear System

In this paper an initial value problem for a non-linear system of two singularly perturbed first order differential equations is considered on the interval (0,1].The components of the solution of this system exhibit initial layers at 0. A numerical method composed of a classical finite difference scheme on a piecewise uniform Shishkin mesh is suggested. This method is proved to be almost first order convergent in the maximum norm uniformly in the perturbation parameters.

scholarly journals GREEN’S MATRICES FOR FIRST ORDER DIFFERENTIAL SYSTEMS WITH NONLOCAL CONDITIONS∗

2017 ◽  
Vol 22 (2) ◽  
pp. 213-227
Author(s):  
Gailė Paukštaitė ◽  
Artūras Štikonas
Keyword(s):  
Differential Equation ◽  
Linear System ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Green's Function ◽  
Nonlocal Conditions ◽  
Differential Systems ◽  
First Order ◽  
Green’S Matrix ◽  
Explicit Representations

In this paper, we investigate the linear system of first order ordinary differential equations with nonlocal conditions. Green’s matrices, their explicit representations and properties are considered as well. We present the relation between the Green’s matrix for the system and the Green’s function for the differential equation. Several examples are also given.

scholarly journals A parameter uniform almost first order convergent numerical method for non-linear system of singularly perturbed differential equations

BIOMATH ◽  
2016 ◽  
Vol 5 (2) ◽  
pp. 1608111
Author(s):  
Ishwariya Raj ◽  
Princy Mercy Johnson ◽  
John J.H Miller ◽  
Valarmathi Sigamani
Keyword(s):  
Linear System ◽  
Differential Equations ◽  
Numerical Method ◽  
Shishkin Mesh ◽  
Singularly Perturbed ◽  
Initial Value ◽  
First Order ◽  
Non Linear ◽  
Perturbation Parameters ◽  
Non Linear System

In this paper an initial value problem for a non-linear system of two singularly perturbed first order differential equations is considered on the interval (0,1].The components of the solution of this system exhibit initial layers at 0. A numerical method composed of a classical finite difference scheme on a piecewise uniform Shishkin mesh is suggested. This method is proved to be almost first order convergent in the maximum norm uniformly in the perturbation parameters.

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