Combinatorial resolution of systems of differential equations, I. Ordinary differential equations

1986 ◽  
pp. 210-245 ◽  
Author(s):  
Pierre Leroux ◽  
Gérard X. Viennot
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Systems Of Differential Equations

scholarly journals DEGENERATE MATRIX METHOD FOR SOLVING NONLINEAR SYSTEMS OF DIFFERENTIAL EQUATIONS

1998 ◽  
Vol 3 (1) ◽  
pp. 45-56
Author(s):  
T. Cîrulis ◽  
O. Lietuvietis
Keyword(s):  
Nonlinear Systems ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Matrix Method ◽  
Iteration Procedure ◽  
Kutta Method ◽  
Runge Kutta Method ◽  
Systems Of Differential Equations ◽  
Runge Kutta ◽  
Degenerate Matrix

Degenerate matrix method for numerical solving nonlinear systems of ordinary differential equations is considered. The method is based on an application of special degenerate matrix and usual iteration procedure. The method, which is connected with an implicit Runge‐Kutta method, can be simply realized on computers. An estimation for the error of the method is given.

scholarly journals Analytical Solutions of Fuzzy Linear Differential Equations in the Conformable Setting

2021 ◽  
Vol 2 (2) ◽  
pp. 13-30
Author(s):  
Awais Younus ◽  
Muhammad Asif ◽  
Usama Atta ◽  
Tehmina Bashir ◽  
Thabet Abdeljawad
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Analytical Solutions ◽  
Higher Order ◽  
Linear Differential Equations ◽  
Conformable Derivative ◽  
Systems Of Differential Equations ◽  
Two Systems ◽  
Linear Differential

In this paper, we provide the generalization of two predefined concepts under the name fuzzy conformable differential equations. We solve the fuzzy conformable ordinary differential equations under the strongly generalized conformable derivative. For the order $\Psi$, we use two methods. The first technique is to resolve a fuzzy conformable differential equation into two systems of differential equations according to the two types of derivatives. The second method solves fuzzy conformable differential equations of order $\Psi$ by a variation of the constant formula. Moreover, we generalize our results to solve fuzzy conformable ordinary differential equations of a higher order. Further, we provide some examples in each section for the sake of demonstration of our results.

Theory and applications of first-order systems of Stieltjes differential equations

2017 ◽  
Vol 6 (1) ◽  
pp. 13-36 ◽  
Author(s):  
Marlène Frigon ◽  
Rodrigo López Pouso
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Time Scales ◽  
Existence And Uniqueness ◽  
Basic Theory ◽  
Dynamic Equations ◽  
Uniqueness Of Solutions ◽  
First Order ◽  
Systems Of Differential Equations ◽  
Set Up

AbstractWe set up the basic theory of existence and uniqueness of solutions for systems of differential equations with usual derivatives replaced by Stieltjes derivatives. This type of equations contains as particular cases dynamic equations on time scales and impulsive ordinary differential equations.

scholarly journals On the Upper Bounds of Eigenvalues for a Class of Systems of Ordinary Differential Equations with Higher Order

2011 ◽  
Vol 2011 ◽  
pp. 1-12 ◽  
Author(s):  
Gao Jia ◽  
Li-Na Huang ◽  
Wei Liu
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Upper Bound ◽  
Upper Bounds ◽  
Higher Order ◽  
Geometric Measure ◽  
Systems Of Differential Equations

The estimate of the upper bounds of eigenvalues for a class of systems of ordinary differential equations with higher order is considered by using the calculus theory. Several results about the upper bound inequalities of the ()th eigenvalue are obtained by the first eigenvalues. The estimate coefficients do not have any relation to the geometric measure of the domain. This kind of problem is interesting and significant both in theory of systems of differential equations and in applications to mechanics and physics.

scholarly journals Minimal and maximal solutions to systems of differential equations with a singular matrix

2003 ◽  
Vol 45 (2) ◽  
pp. 223-231
Author(s):  
Tadeusz Jankowski
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Monotone Iterative Technique ◽  
Extremal Solutions ◽  
Iterative Technique ◽  
Singular Matrix ◽  
Monotone Iterative ◽  
Maximal Solutions ◽  
Systems Of Differential Equations ◽  
Minimal And Maximal Solutions

AbstractThe monotone iterative technique is applied to a system of ordinary differential equations with a singular matrix. The existence of extremal solutions is proved.

scholarly journals On Osculating Systems of Differential Equations of Type (N, 1, 2)

1968 ◽  
Vol 31 ◽  
pp. 251-278 ◽  
Author(s):  
Hisasi Morikawa
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Linear Systems ◽  
Present Article ◽  
Point Of View ◽  
Main Subject ◽  
Systems Of Differential Equations ◽  
Projective Point

The main subject in the present article has the origin in the following quite primitive question: Linear systems of ordinary differential equations form a nice family. Then, from the projective point of view, what does correspond to linear systems?

CONVODE: A REDUCE PACKAGE FOR DIFFERENTIAL EQUATIONS

1993 ◽  
Vol 04 (02) ◽  
pp. 365-374
Author(s):  
ALAIN MOUSSIAUX ◽  
RICHARD MAIRESSE
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Systems Of Differential Equations

The package CONVODE (CONVersion of Ordinary Differential Equations) is written in REDUCE 3.4 in order to study differential equations and systems of differential equations. Differential equations (D.E.) whose solutions can be obtained using CLASSICAL methods of integration are investigated. CONVODE is written on the framework of most of the textbook on D.E. One of the characteristics of CONVODE is to be a very wordy program and to keep its user aware of its process.

ON A CONNECTION BETWEEN A CLASS OF SYSTEMS OF ORDINARY DIFFERENTIAL EQUATIONS AND INTEGRAL OPERATORS WITH SEMI-SEPARABLE KERNEL

2018 ◽  
Vol 52 (2 (246)) ◽  
pp. 77-83
Author(s):  
A.H. Hovhannisyan ◽  
A.H. Kamalyan ◽  
H.A. Kamalyan
Keyword(s):  
Integral Operator ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Fundamental Matrix ◽  
Integral Operators ◽  
Systems Of Differential Equations ◽  
Separable Kernel

In the present paper the connection between a class of systems of differential equations and integral operators with semi-separable kernel is established. Using a matrix of the system the inverse to a given integral operator is constructed. Moreover by putting some additional conditions on the kernel of integral operator and by the help of inverse of integral operator a fundamental matrix of the system is constructed.

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