Solutions For System Of Equations Research Articles

An Application of the Fixed Point Theory to the Study of Monotonic Solutions for Systems of Differential Equations

In this paper, we establish some conditions for the existence and uniqueness of the monotonic solutions for nonhomogeneous systems of first-order linear differential equations, by using a result of the fixed points theory for sequentially complete gauge spaces.

Fractional Hybrid Differential Equations and Coupled Fixed-Point Results for α -Admissible F ψ 1 , ψ 2 − Contractions in M − Metric Spaces

In this paper, we investigate the existence of a unique coupled fixed point for α − admissible mapping which is of F ψ 1 , ψ 2 − contraction in the context of M − metric space. We have also shown that the results presented in this paper would extend many recent results appearing in the literature. Furthermore, we apply our results to develop sufficient conditions for the existence and uniqueness of a solution for a coupled system of fractional hybrid differential equations with linear perturbations of second type and with three-point boundary conditions.

A coupled system of Langevin differential equations of fractional order and associated to antiperiodic boundary conditions

In this paper, we provide an extension result for the existence and uniqueness of solutions for a coupled system of fractional Langevin differential equations with antiperiodic boundary conditions. The system involves two different Caputo fractional derivatives defined on different intervals and associated with boundary conditions described by sequential fractional derivatives. As a conclusion for our main result, we deduce the results of H. Fazli, J.J. Nieto, Fractional Langevin equation with anti‐periodic boundary conditions, Chaos Soliton Fract, 114 (2018),332–337 under less restrictive conditions. The consistency of the main results is demonstrated by two numerical examples. For the sake of completeness, we end the paper by a concluding discussion.

Mild solutions for a coupled system of fractional differential equations with slit-strips type integral boundary conditions

In this present paper, we study the existence and uniqueness of solutions for a coupled system of fractional differential equations with Banach contraction mapping principle and Leray-Schauder alternative theorem. Examples are given to illustrate the applicability of the obtained results.

Some Fixed Point Theorems for $$F(\psi,\varphi)$$-Contractions and Their Application to Fractional Differential Equations

The main object of this paper is to establish some fixed point results for $$F(\psi,\varphi)$$ -contractions in partially-ordered metric spaces. As an application of one of these fixed point theorems, we discuss the existence of a unique solution for a coupled system of higher-order fractional differential equations with multi-point boundary conditions. The results presented in this paper are shown to extend many recent results appearing in the literature.

Approximate Methods for Solving Linear and Nonlinear Hypersingular Integral Equations

We propose an iterative projection method for solving linear and nonlinear hypersingular integral equations with non-Riemann integrable functions on the right-hand sides. We investigate hypersingular integral equations with second order singularities. Today, hypersingular integral equations of this type are widely used in physics and technology. The convergence of the proposed method is based on the Lyapunov stability theory of solutions of ordinary differential equation systems. The advantage of the method for linear equations is in simplicity of unique solvability verification for the approximate equations system in terms of the operator logarithmic norm. This makes it possible to estimate the norm of the inverse matrix for an approximating system. The advantage of the method for nonlinear equations is that neither the existence or reversibility of the nonlinear operator derivative is required. Examples are given illustrating the effectiveness of the proposed method.

Bessel functions of two variables as solutions for systems of the second order differential equations

Bessel functions of two variables as solutions for systems of the second order differential equations

Existence and uniqueness results for a coupled system of nonlinear fractional differential equations with two fractional orders

In this work, we discuss the existence of solutions for a coupled system of nonlinear fractional differential equations involving two Riemann-Liouville fractional orders. By applying the Leray-Schauder’s nonlinear alternative and Banach’s fixed-point theorem the existence and uniqueness of solutions is obtained.

Acceleration and higher-order analyses solved by extending the superposition principle: The incipient motion technique

The superposition principle, when applicable in the kinematic analysis of a mechanism, makes it possible to relate the studied mechanism with its component structures, and reduces the computation burden by exploiting the relationships among different data sets. Acceleration and higher-order analyses of holonomic or first-order non-holonomic mechanisms, and the velocity analysis of mechanisms with time-dependent (rheonomic) constraints need the solution of linear and non-homogeneous equation systems. The non-homogeneity of these problems forbids the use of the superposition principle to solve them. In this work, a novel kinematic-analysis technique (Incipient Motion Technique) that fully exploits the properties of linear and non–homogeneous equation systems is proposed. This solution technique has advantages similar to the ones of the superposition principle, holds for rheonomus systems, too, is efficient enough to use it in general purpose programs for multibody dynamics analysis, and is simple enough to present it in courses for graduate students.

METHOD OF FAST MATRIX MULTIPLICATION UNDER ARM ARCHITECTURE USING SIMD INSTRUCTIONS

Background. Matrix multiplication is a rather complicated algorithm with a large number of operations. An additional problem is the nonlinear memory traversal of matrices. Matrix multiplication is widely used in various fields, such as neural networks, solutions of linear equation systems, matrix transformations, and so on. Therefore, it is important to develop a method of matrix multiplication, which will take into account the problems of the location of the matrices in memory, and will effectively manage the data when reused.Objective. The purpose of the paper is to develop a method of fast matrix multiplication of two matrices, as well as multiplying the matrix by the transposed matrix and by a list of vectors (including special case for only one vector), as well as to implement it as a function with optimization for ARM architecture processors. The function must be able to handle different types of data and submatrices. The integer result can be scaled.Methods. The main ideas of the developed method are simultaneous work with several rows/columns of input matrices and their splitting into blocks, which will allow the algorithm to run on the same memory for a while. The C programming language was chosen for implementation. SIMD instructions were used to increase productivity. We also need to properly organize the memory preloading for effective implementation under the ARM architecture.Results. A function that performs matrix multiplication by the developed method with the necessary parameters was implemented as a result of the study. Tests on various sizes and types have shown that the implemented function is faster than analogues from the OpenCV2 and Eigen 3 libraries. Testing was done using the vipmed utility for running and measuring features developed for enterprise use at VIT.Conclusions. The proposed matrix multiplication method gives the expected acceleration of matrix multiplication operations, has passed evaluation test for use and meets the target requirements. For further work, it is necessary to study in more detail the influence of the cache at different levels and compare with other existing libraries.

Using Bernstein multi-scaling polynomials to obtain numerical solution of Volterra integral equations system

In this paper, first, Bernstein multi-scaling polynomials (BMSPs), which are generalization of Bernstein polynomials (BPs), are introduced and some of their properties are explained. Then, a new method based on BMSPs to achieved numerical solution for system of nonlinear integral equations is proposed. The proposed method converted the system of integral equations to a nonlinear system. To evaluate the efficiency of the proposed method, some systems of nonlinear integral equations are solved, and their numerical solutions are compared with other similar methods.

Existence Solution for Nonlinear System of Fractional Integrodifferential Equations of Volterra Type with Fractional Boundary Conditions

This article investigates existence, uniqueness and stability solutions of new fractional Volterra integro-differential equations system with fractional boundary conditions by using the existence and uniqueness theorem. Theorems on existence and uniqueness of solution are established under some necessary and sufficient conditions on compact space. A simple example of application of the main results of this article is presented.

EXISTENCE, UNIQUENESS AND STABILITY SOLUTIONS FOR NEW NONLINEAR SYSTEM OF INTEGRO-DIFFERENTIAL EQUATIONS OF VOLTERRA TYPE

In this article, we established the existence, uniqueness and stability solutions for a nonlinear system of integro-differential equations of Volterra type in Banach spaces. Krasnoselskii Fixed point theorems and Picard approximation method are the main tool used here to establish the existence and uniqueness results. A simple example of application of the main result of this paper is presented.

Solutions for nonlinear systems of integro-differential equations that contain multiple integrals of (V F) and (F V) types with isolated singular kernels.

Solutions for nonlinear systems of integro-differential equations that contain multiple integrals of (V F) and (F V) types with isolated singular kernels.

Solitary wave solutions and traveling wave solutions for systems of time-fractional nonlinear wave equations via an analytical approach

This paper introduces a new approximate-analytical approach for solving systems of Fractional Nonlinear Partial Differential Equations (FNPDEs). However, the main advantage of this new approximate-analytical approach is to obtain the analytical solution for general systems of FNPDEs in forms of convergent series with easily computable components using Caputo fractional partial derivative. Moreover, the convergence theorem and error analysis of the proposed method are also shown. Solitary wave solutions and traveling wave solutions for the system of fractional dispersive wave equations and the system of fractional long water wave equations are successfully obtained. The numerical solutions are also obtained in forms of tables and graphs to confirm the accuracy and efficiency of the suggested method.

Global stability of traveling waves for delay reaction-diffusion systems without quasi-monotonicity

In this article, we consider the existence of positive solutions for a nonlinear system of fourth-order ordinary differential equations. By constructing a single cone \(P\) in the product space \(C[0, 1] \times C[0, 1]\) and applying fixed point theorem in cones, we establish the existence of positive solutions for a system in which the nonlinear terms are both superlinear or sublinear. In addition, by the construction of the product cone \(K_1 \times K_2 \subset C[0, 1] \times C[0, 1]\) along with the product formula of fixed point theory on a product cone, we investigate the existence of positive solutions involving nonlinear terms, one uniformly superlinear or sublinear, and the other locally uniformly sublinear or superlinear.
 For more information see https://ejde.math.txstate.edu/Volumes/2020/45/abstr.html

Existence and uniqueness of periodic solutions for a system of differential equations via operator methods

This article investigates the existence and uniqueness of periodic solutions for a new system of differential equations. By employing fixed point theorems for increasing φ-(h,tau )-concave operators, we establish the existence of unique periodic solution for our differential system and then give a monotone iterative scheme to approximate the unique periodic solution. Some examples are presented in the end to illustrate the validity of our main results.

Existence of solution for system of differential equations in $$c_{0}$$ and $$\ell _{1}$$ spaces

The paper considers the system of second order differential equations of the form: $$\begin{aligned} \frac{\mathrm {d}^2v_{j}}{\mathrm {d}t^2}-v_{j}=f_{j}(t,v(t));~~~v_{j}(0)=v_{j}(T)=0 \end{aligned}$$ where $$t\in [0,T]$$ , $$v(t)=\left( v_{j}(t)\right) _{j=1}^{\infty }$$ . The system is investigated in Banach spaces $$c_{0}$$ and $$\ell _{1}$$ . Using the concept of measures of noncompactness, conditions for the existence of solution are found for the above system. The idea is supported with different examples.

Existence, uniqueness and stability solutions for nonlinear systems of differential equations with higher derivatives

Existence, uniqueness and stability solutions for nonlinear systems of differential equations with higher derivatives

Study of Entropy Properties of a Linearized Version of Godunov’s Method

The ideas of formulating a weak solution for a hyperbolic system of one-dimensional gas dynamics equations are presented. An important aspect is the examination of the scheme for the fulfillment of the nondecreasing entropy law, which must hold for weak solutions and is obligatory from a physics point of view. The concept of a weak solution is defined in a finite-difference formulation with the help of the simplest linearized version of the classical Godunov scheme. It is experimentally shown that this version guarantees an entropy nondecrease. As a result, the growth of entropy on shock waves can be simulated without using any correction terms or additional conditions.