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Bounded index, entire solutions of ordinary differential equations and summability methods

A brief survey of recent results on functions of bounded index and bounded index summability methods is given. Theorems on entire solutions of ordinary differential equations with polynomial ... I nternat. J. Math. & Math. Si. Vol. BOUNDED INDEX, ENTIRE SOLUTIONS OF ORDINARY DIFFERENTIAL EQUATIONS AND SUMMABILITY METHODS G.H. FRICKE 0 1 2 Ee Solutions. 0 Department of Mathematics University

Linear Operators and the General Solution of Elementary Linear Ordinary Differential Equations

We make use of linear operators to derive the formulae for the general solution of elementary linear scalar ordinary differential equations of order n. The key lies in the factorization of the linear ... introductory course on ordinary differential equations. The method is based on the integral operator as defined in Definition 2.3. and also applies to linear differential equations with nonconstant coefficients

Homoclinic solutions for linear and linearizable ordinary differential equations

(French). MR 99i:34082. [9] M. Cecchi , M. Marini , and P. L. Zezza , An abstract method for nonlinear boundary value problems on noncompact intervals , Ordinary Differential Equations and Functional ... . Zbl 283 . 34052 . [12] , On nonlinear functional perturbation problems for ordinary differential equations , J. Differential Equations 12 ( 1972 ), 63 - 80 . MR 48#6574. Zbl 243 . 34015 . [13] A. G

k-component disconjugacy for systems of ordinary differential equations

Disconjugacy of the kth component of the mth order system of nth order differenttal equations Y(n)=f(x,Y,Y′,…,Y(n−1)), (1.1), is defined, where f(x,Y1,…,Yn), ∂f∂yij(x,Y1,…,Yn):(a,b)×Rmn→Rm are ... variational equation z(n) ?n..i=ifyi( x' 0(x), Y0(n-l)(x)) Z (i-l), (1.2), is also studied. - K-COMPONENT DISCONJUGACY FOR SYSTEMS OF ORDINARY DIFFERENTIAL EQUATIONS Conditions are given for continuous

Model selection via marginal likelihood estimation by combining thermodynamic integration and gradient matching

Conducting statistical inference on systems described by ordinary differential equations (ODEs) is a challenging problem. Repeatedly numerically solving the system of equations incurs a high ... supplementary material, which is available to authorized users. 1 Introduction Ordinary differential equations (ODEs) are a powerful way of providing an observed system with a mathematical description. The

A Spreadsheet Solution of a System of Ordinary Differential Equations Using the Fourth-Order Runge-Kutta Method

Solving systems of ordinary differential equations (ODEs) by using the fourth-order Runge-Kutta (RK4) method in classroom or in examinations is quite tedious, tiring and boring since it involves many ... system of ordinary differential equations (ODEs). There are several available numerical methods used to solve ODEs such as Euler’s method, second-order Runge-Kutta (RK2) method and fourth-order Runge-Kutta

Reducible functional differential equations

This is the first part of a survey on analytic solutions of functional differential equations (FDE). Some classes of FDE that can be reduced to ordinary differential equations are considered since ... ) are satisfied, then every p-times differentiable solution of Eq. (2.14) is a component of the solution of a system of ordinary differential equations with argument t only. This system is obtained from

Distributional and entire solutions of ordinary differential and functional differential equations

A brief survey of recent results on distributional and entire solutions of ordinary differential equations (ODE) and functional differential equations (FDE) is given. Emphasis is made on linear ... mentioned. AND PHRASES; Ordinary Differential Equations; Functional Differential - DISTRIBUTIONAL AND ENTIRE SOLUTIONS OF ORDINARY DIFFERENTIAL AND FUNCTIONAL DIFFERENTIAL EQUATIONS I. INTRODUCTION AND

Agent-Based Fabric Modeling Using Differential Equations

harmonic motion to textiles and fashion, fields not typically discussed in the undergraduate differential equations classroom. Euler's method is coded into the model to solve a system of ordinary ... ′′ = −k2(x2 − x1) + k3x2, as (x2 − x1) determines the length of the spring between the two masses. k1 m1 m2 k3 k2 P 3 We now have a system of ordinary differential equations whose solutions, x1(t ) and x2

Characterization of several classes of second-order ODEs by using differential invariants

Several classes of second-order ordinary differential equations are characterized intrinsically by means of differential invariants. The method is proved to be computationally feasible. ... polynomial time. The problem of characterization of ordinary differential equations has been tackled by some authors in the last decades (see, e.g., [ 5, 17, 18, 20, 22, 23, 26, 27, 34, 35 ]). All these

Existence of positive radial solutions for a weakly coupled system via blow up

The existence of positive solutions to certain systems of ordinary differential equations is studied. Particular forms of these systems are satisfied by radial solutions of associated partial ... partial differential equations. In this paper we will study existence of positive solutions to a system of the form System (D) is particularly important when the homeomorphisms φi take the form φi(s) = sai

A fourth-order Runge-Kutta (RK4) Spreadsheet Calculator For Solving A System of Two First-Order Ordinary Differential Equations Using Visual Basic (VBA) Programming

Motivated by the work of a spreadsheet solution of a system of ordinary differential equations (ODEs) using the fourth-order Runge-Kutta (RK4) method, a RK4 spreadsheet calculator for solving a ... ] Leon, S. B. y., Uifig, R. & Blandcard, J. (1996). Teaching the numerical Solution of ordinary Differential Equations Using Excel 5.0. Computer Application in Engineering Education. 5(2): Pg 117-125. [2

Decomposition of ordinary differential equations

Decompositions of linear ordinary differential equations (ode’s) into components of lower order have successfully been employed for determining their solutions. Here this approach is generalized to ... differential equations are suggested. Ordinary differential equations; Decomposition; Exact solutions - Ever since its introduction more than 300 years ago the concept of a differential equation, and

Teaching Differential Equations with Modeling and Visualization

In this article, I explain the history of using Interdisciplinary Lively Applications Projects (ILAPs) in an ordinary differential equations course. Students want to learn methods to "solve real ... Small at West Point, I gave a group of students a differential equations problem in the form of a long word problem and asked them to set up the model (define variables, state what is given, make a few

Using Technology in a Differential Equations Course: Lessons Learned Implementing a New Paradigm

Historically, a first course in Ordinary Differential Equations (ODEs) has been taught as a “methods course.” Namely, different types of differential equations are trotted out and the method of ... Background Differential Equations is a four credit hour course in the mathematics curriculum at Benedictine University. Students usually take it after taking multivariate calculus and before (or along with

Local existence result of the single dopant diffusion including cluster reactions of high order

nonlinear system of reaction-drift-diffusion equations, a nonlinear system of ordinary differential equations in Banach spaces, and a nonlinear elliptic equation for the electrochemical potential. The local ... satisfies (P) for some Tf ∈ (0, ∞). 4. Ordinary differential equations In this section, we consider the system of ordinary differential equations in Banach spaces (2.7) and (2.8). For given functions (Ck)k

A Simplified Model of the Internal Combustion Engine

This project further investigates a model of a simplified internal combustion engine considered by Kranc in 1977. Using Euler’s method for ordinary differential equations, we modeled the interaction ... ordinary differential equations. MATHEMATICAL DESCRIPTION AND SOLUTION APPROACH Before discussing the mathematics of the problem it is important to understand the concepts behind the movement of a two

Efficient Two-Derivative Runge-Kutta-Nyström Methods for Solving General Second-Order Ordinary Differential Equations

efficiency of the new methods. 1. Introduction In this article, we are interested in initial value problems (IVPs) of second-order ordinary differential equations (ODEs):where are continuous vector valued ... Computational Approach, Library of Engineering Mathematics, CRC Press, Boca Raton, Fla, USA, 1996. View at MathSciNetE. Hairer, S. P. Nørsett, and G. Wanner, Solving Ordinary Differential Equations I: Nonstiff

An Analysis of Unsolvable Linear Partial Differential Equations of Order One

based on the discovery by Leonard Euler that certain differential equations, called ordinary differential equations (ODEs), are indeed always solvable. While ODEs deal with simple conditions, under which ... , Fayetteville , USA Follow this and additional works at: Part of the Ordinary Differential Equations and Applied Dynamics Commons Recommended Citation - AN ANALYSIS OF

Bäcklund transformations for several cases of a type of generalized KdV equation

type of Bäcklund transformation for several specific cases of the power of the derivative term appearing in the equation. In the process, several interesting, new, ordinary, differential equations are ... Theorem 1 for several values of the power n in (5). This method is of interest in itself, and in developing it, leads to other types of ordinary differential equations which must be integrated to produce