scholarly journals Reduction method for solving Boundary Value Problem on Graph to it's internal edge: طريقة التخفيض لحل مسألة قيم حدية على البيان إلى ضلع داخلي منه

2019 ◽  
Vol 3 (4) ◽  
Author(s):  
Amane Abu Alkhair Almalla, Berlent Sabry Mattit, Moaaz Ali A
Keyword(s):  
Differential Equation ◽  
Boundary Value Problem ◽  
Existence And Uniqueness ◽  
Reduction Method ◽  
Boundary Value ◽  
Geometric Graph ◽  
Internal Edge ◽  
Original Graph ◽  
The Right ◽  
Reduced Problem

  The main aim to this research is to reduce the boundary value problem for fourth differential equation on geometric graph with cycles to a problem on a internal edge provided that the right hand side of the differential equation is identically zero on some subgraph of the original graph, and in this research we find the sign of some coefficients in the boundary conditions of the reduced problem and relationship between these coefficients. That's helping us to prove existence and uniqueness for a boundary value problem resulting from this reduction. In order to reach our desired goal, we study the reduction method of boundary value problem for fourth differential equation on tree geometric graph(no cycles), finally we can say that our research help us to study green function on edge(interval) instead of complex sty ding on geometric graph(with cycles).    

A Method for the Numerical Solution of a Boundary Value Problem for a Linear Differential Equation with Interval Parameters

2019 ◽  
Vol 16 (07) ◽  
pp. 1850115 ◽  
Author(s):  
Nizami A. Gasilov ◽  
Müjdat Kaya
Keyword(s):  
Differential Equation ◽  
Boundary Value Problem ◽  
Linear Differential Equation ◽  
Numerical Method ◽  
Boundary Value ◽  
Real Life ◽  
Boundary Values ◽  
Right Hand ◽  
Linear Differential ◽  
The Right

In many real life applications, the behavior of the system is modeled by a boundary value problem (BVP) for a linear differential equation. If the uncertainties in the boundary values, the right-hand side function and the coefficient functions are to be taken into account, then in many cases an interval boundary value problem (IBVP) arises. In this study, for such an IBVP, we propose a different approach than the ones in common use. In the investigated IBVP, the boundary values are intervals. In addition, we model the right-hand side and coefficient functions as bunches of real functions. Then, we seek the solution of the problem as a bunch of functions. We interpret the IBVP as a set of classical BVPs. Such a classical BVP is constructed by taking a real number from each boundary interval, and a real function from each bunch. We define the bunch consisting of the solutions of all the classical BVPs to be the solution of the IBVP. In this context, we develop a numerical method to obtain the solution. We reduce the complexity of the method from [Formula: see text] to [Formula: see text] through our analysis. We demonstrate the effectiveness of the proposed approach and the numerical method by test examples.

On the differential equation governing the rear stagnation point in magnetohydrodynamics and Goldstein's ‘backward’ boundary layers

1967 ◽  
Vol 63 (4) ◽  
pp. 1327-1330 ◽  
Author(s):  
S. Leibovich
Keyword(s):  
Differential Equation ◽  
Boundary Value Problem ◽  
Stagnation Point ◽  
Boundary Layers ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Stagnation Point Flow ◽  
Special Cases ◽  
Rear Stagnation Point

AbstractExistence and uniqueness proofs for a boundary-value problem associated with a magnetohydrodynamic Falkner–Skan equation are presented. Relevant special cases of the problem herein considered include the magnetohydrodynamic rear stagnation point flow, and the non-magnetic ‘backward boundary layers’ of Goldstein(2).

scholarly journals Global theorem of existence and uniqueness of the firstboundary value problem for nonlinear integrodifferential equations ofparabolic type

2017 ◽  
Vol 21 (3) ◽  
pp. 64-72
Author(s):  
O.P. Filatov
Keyword(s):  
Boundary Value Problem ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Parabolic Type ◽  
Current Application ◽  
Real Model ◽  
Fuel Tanks ◽  
The Difference ◽  
The Right ◽  
A Current

Global theorem of existence and uniqueness of solution of the first boundary value problem for nonlinear integrodifferential equation of parabolic type is proved. If the right-hand side of the equation is integrally bounded, then we have estimate of the norm of the difference of two solutions, which implies continuous dependence of solution on the initial function and uniqueness of so- lution of the first boundary value problem. The problem under consideration generalizes the real model for measuring the level of incompressible fluid in the fuel tanks missiles. Therefore, such problem have a current application.

One method for investigating the solvability of boundary value problems for an implicit differential equation

2021 ◽  
pp. 404-413
Author(s):  
Wassim Merchela
Keyword(s):  
Differential Equation ◽  
Boundary Value Problem ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Linear Boundary ◽  
Implicit Differential Equation ◽  
Carathéodory Conditions ◽  
Covering Set ◽  
The Right ◽  
Scalar Differential Equation

The article concernes a boundary value problem with linear boundary conditions of general form for the scalar differential equation f(t,x(t),x ̇(t))=y ̂(t), not resolved with respect to the derivative x ̇ of the required function. It is assumed that the function f satisfies the Caratheodory conditions, and the function y ̂ is measurable. The method proposed for studying such a boundary value problem is based on the results about operator equation with a mapping acting from a metric space to a set with distance (this distance satisfies only one axiom of a metric: it is equal to zero if and only if the elements coincide). In terms of the covering set of the function f(t,x_1,•): R→R and the Lipschitz set of the function f(t,•,x_2): R →R, conditions for the existence of solutions and their stability to perturbations of the function f generating the differential equation, as well as to perturbations of the right-hand sides of the boundary value problem: the function y ̂ and the value of the boundary condition, are obtained.

On the existence and uniqueness of a positive solution to a boundary value problem for a nonlinear ordinary differential equation of even order

2021 ◽  
pp. 341-347
Author(s):  
Gusen E. Abduragimov ◽  
Patimat E. Abduragimova ◽  
Madina M. Kuramagomedova
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Boundary Value Problem ◽  
Positive Solution ◽  
Existence And Uniqueness ◽  
Initial Conditions ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Nonlinear Ordinary Differential Equation ◽  
Even Order

In the article, we consider a boundary value problem for a nonlinear ordinary differential equation of even order which, obviously, has a trivial solution. Sufficient conditions for the existence and uniqueness of a positive solution to this problem are obtained. With the help of linear transformations of T. Y. Na [T. Y. Na, Computational Methods in Engineering Boundary Value Problems, Acad. Press, NY, 1979, ch. 7], the boundary value problem is reduced to the Cauchy problem, the initial conditions of which make it possible to uniquely determine the transformation parameter. It is shown that the transformations of T. Y. Na uniquely determine the solution of the original problem. In addition, based on the proof of the uniqueness of a positive solution to the boundary value problem, a sufficiently effective non–iterative numerical algorithm for constructing such a solution is obtained. A corresponding example is given.

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