scholarly journals Differential Equations: Between the Theoretical Sublimation and the Practical Universalization

2019 ◽  
Vol 21 (1) ◽  
Author(s):  
Juan Eduardo Nápoles Valdez
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
The Other ◽  
The One

In this paper, we present, briefly, the bifront character of the ordinary differential equations (ODE): on the one hand the theoretical specialization in different areas and on the other, the multiplicity of applications of the same, as well as some reflections on the development of a course of ode in this context.

scholarly journals Symmetries and the inverse problem of Lagrangian dynamics for linear systems

1983 ◽  
Vol 25 (2) ◽  
pp. 232-243 ◽  
Author(s):  
W. Sarlet
Keyword(s):  
Inverse Problem ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Linear Systems ◽  
The Other ◽  
Time Dependent ◽  
Lagrangian Mechanics ◽  
Lagrangian Dynamics ◽  
The One ◽  
General Time

AbstractWe discuss general, time-dependent, linear systems of second-order ordinary differential equations. A study is made of the similarities and discrepancies between the inverse problem of Lagrangian mechanics on the one hand, and the search for linear dynamical symmetries on the other hand.

EQUIVALENCE OF THE TWO METHODS IN CALCULATING THE EQUILIBRIUM SHAPES OF CYLINDRICAL VESICLES

1999 ◽  
Vol 13 (16) ◽  
pp. 547-553
Author(s):  
SHAOGUANG ZHANG ◽  
ZHONGCAN OUYANG ◽  
JIXING LIU
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
The Other ◽  
General Shape ◽  
Calculus Of Variation ◽  
And Topology ◽  
Shape Equation ◽  
Equilibrium Shapes ◽  
Comparison Of The Results ◽  
The Relationship

So far, two methods are often used in solving the equilibrium shapes of vesicles. One method is by starting with the general shape equation and restricting it to the shapes with particular symmetry. The other method is by assuming the symmetry and topology of the vesicle first and treating it with the calculus of variation to get a set of ordinary differential equations. The relationship between these two methods in the case of cylindrical vesicles, and a comparison of the results are given.

scholarly journals Algebraic approach for the one-dimensional Dirac–Dunkl oscillator

2020 ◽  
Vol 35 (31) ◽  
pp. 2050255
Author(s):  
D. Ojeda-Guillén ◽  
R. D. Mota ◽  
M. Salazar-Ramírez ◽  
V. D. Granados
Keyword(s):  
Energy Spectrum ◽  
Irreducible Representation ◽  
Differential Equations ◽  
Representation Theory ◽  
Algebraic Approach ◽  
The Other ◽  
One Dimensional ◽  
The One

We extend the (1 + 1)-dimensional Dirac–Moshinsky oscillator by changing the standard derivative by the Dunkl derivative. We demonstrate in a general way that for the Dirac–Dunkl oscillator be parity invariant, one of the spinor component must be even, and the other spinor component must be odd, and vice versa. We decouple the differential equations for each of the spinor component and introduce an appropriate su(1, 1) algebraic realization for the cases when one of these functions is even and the other function is odd. The eigenfunctions and the energy spectrum are obtained by using the su(1, 1) irreducible representation theory. Finally, by setting the Dunkl parameter to vanish, we show that our results reduce to those of the standard Dirac-Moshinsky oscillator.

scholarly journals Researches in physical astronomy

1837 ◽  
Vol 3 ◽  
pp. 101-102
Keyword(s):  
Differential Equations ◽  
The Other ◽  
Variation Of Parameters ◽  
First Approximation ◽  
The One ◽  
Equivalent Method

For the solution of mechanical problems, two methods in general present themselves: the one furnished by the variation of parameters, or constants, which complete the integral obtained by the first approximation,—the other furnished by the integration of the differential equations by means of indeterminate coefficients, or some equivalent method. Each of these methods is applicable to the theory of the perturbations of the heavenly bodies, and they lead to expressions which are of course substantially identical, but which do not appear in the same shape except after certain transformations. The object of the author in the present paper is to effect transformations, by which their identity is established, making use of the developments given in his former papers, published in the Philosophical Transactions. The identity of the results obtained by either methods affords a confirmation of the exactness of those expressions.

A Novel Method for Solving Consistency-Order Initial Value of Ordinary Differential Equations

2014 ◽  
Vol 543-547 ◽  
pp. 1844-1847
Author(s):  
Si Min Zhu ◽  
Hai Yun Deng ◽  
Kai Zheng ◽  
Hua Mei Li ◽  
Xiao Zhou Chen
Keyword(s):  
Differential Equations ◽  
Initial Value Problem ◽  
Integral Formula ◽  
Absolute Error ◽  
The Other ◽  
It Use ◽  
Initial Value ◽  
Novel Method ◽  
The One ◽  
Legendre Quadrature

It is known that the level of the consistency-order of initial value problem is an important standard to determine whether the constructed methods for solving initial value problem of ODEs is suitable or not. There are two methods to solve the consistency-order of initial value problem in general. The one is using the remainder of integral formula as local truncated error, and the other one is using absolute error as local truncated error. In the paper, we propose a novel method based on Gauss-Legendre quadrature formula. It use the method of the remainder of integral formula as local truncated error exists in most of the literatures, and it will be solved once again for the consistency-order of the constructed methods that exist in currently literatures by using absolute error as local truncated error, and then draw a conclusion that is differ from what has been proved correspondingly.

scholarly journals Solving Nonstiff Higher-Order Ordinary Differential Equations Using 2-Point Block Method Directly

2014 ◽  
Vol 2014 ◽  
pp. 1-13 ◽  
Author(s):  
Hazizah Mohd Ijam ◽  
Mohamed Suleiman ◽  
Ahmad Fadly Nurullah Rasedee ◽  
Norazak Senu ◽  
Ali Ahmadian ◽  
...  
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Difference Method ◽  
Divided Difference ◽  
Approximate Solutions ◽  
Higher Order ◽  
Numerical Results ◽  
The Other ◽  
Block Method ◽  
Better Than

We describe the development of a 2-point block backward difference method (2PBBD) for solving system of nonstiff higher-order ordinary differential equations (ODEs) directly. The method computes the approximate solutions at two points simultaneously within an equidistant block. The integration coefficients that are used in the method are obtained only once at the start of the integration. Numerical results are presented to compare the performances of the method developed with 1-point backward difference method (1PBD) and 2-point block divided difference method (2PBDD). The result indicated that, for finer step sizes, this method performs better than the other two methods, that is, 1PBD and 2PBDD.

Exact Equations for the Inextensional Deformation of Cantilevered Plates

1979 ◽  
Vol 46 (3) ◽  
pp. 631-636 ◽  
Author(s):  
J. G. Simmonds ◽  
A. Libai
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Initial Conditions ◽  
Independent Set ◽  
Straight Edge ◽  
The Other ◽  
Subsequent Paper ◽  
First Order ◽  
Alternate Forms ◽  
Approximate Equations

A set of first-order ordinary differential equations with initial conditions is derived for the exact, nonlinear, inextensional deformation of a loaded plate bounded by two straight edges and two curved ones. The analysis extends earlier approximate work of Mansfield and Kleeman, Ashwell, and Lin, Lin, and Mazelsky. For a plate clamped along one straight edge and subject to a force and couple along the other, there are 13 differential equations, but an independent set of 9 may be split off. In a subsequent paper, we consider alternate forms of these 9 equations for plates that twist as they deform. Their structure and solutions are compared to Mansfield’s approximate equations and particular attention is given to tip-loaded triangular plates.

An introduction to numerical methods for stochastic differential equations

Acta Numerica ◽  
1999 ◽  
Vol 8 ◽  
pp. 197-246 ◽  
Author(s):  
Eckhard Platen
Keyword(s):  
Numerical Analysis ◽  
Numerical Methods ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
The Other ◽  
Weak Approximation ◽  
Approximation Methods ◽  
Unified Framework ◽  
Stochastic Nature ◽  
The One

This paper aims to give an overview and summary of numerical methods for the solution of stochastic differential equations. It covers discrete time strong and weak approximation methods that are suitable for different applications. A range of approaches and results is discussed within a unified framework. On the one hand, these methods can be interpreted as generalizing the well-developed theory on numerical analysis for deterministic ordinary differential equations. On the other hand they highlight the specific stochastic nature of the equations. In some cases these methods lead to completely new and challenging problems.

scholarly journals Researches in physical astronomy

1837 ◽  
Vol 3 ◽  
pp. 128-129
Keyword(s):  
Differential Equations ◽  
The Other ◽  
Disturbing Function ◽  
Direct Integration ◽  
Planetary Theory ◽  
The Moon ◽  
Disturbing Force ◽  
Other Hand ◽  
The Stability ◽  
The One

The present paper contains some further developments of the theory of the moon, which are given at length, in order to save the trouble of the calculator, and to avoid the danger of mistake. The author remarks, that while it seems desirable, on the one hand, to introduce into the science of physical astronomy a greater degree of uniformity, by bringing to perfection a theory of the moon founded on the integration of the equations employed in the planetary theory, it is also no less important, on the other hand, to complete, in the latter, the method hitherto applied solely to the periodic inequalities. Hi­therto those terms in the disturbing function which give rise to the secular inequalities, have been detached, and the stability of the system has been inferred by means of the integration of certain equations, which are linear when the higher powers of the eccentri­cities are neglected and from considerations founded on the varia­tion of the elliptic constants. But the author thinks that the stability of the system may be inferred also from the expressions which result at once from the direct integration of the differential equations. The theory, he states, may be extended, without any analytical difficulty, to any power of the disturbing force, or of the eccentricities, ad­mitting the convergence of the series; nor does it seem to be limited by the circumstance of the planet’s moving in the same direction.

scholarly journals Numerical Solution of Equations of the Diffusion Type with Diffusivity Concentration?Dependent. II.

1957 ◽  
Vol 10 (1) ◽  
pp. 29 ◽  
Author(s):  
JR Philip
Keyword(s):  
Differential Equations ◽  
Numerical Solution ◽  
Ordinary Differential Equations ◽  
Diffusion Type ◽  
Solution Of Equations ◽  
The One

A new procedure is developed for the numerical solution of the equation with D and K single-valued functions of ? and the conditions ? = ?n, t=0, x>0; ?=?0 , x = 0, t:> 0. Difficulties inherent in the one method previously suggested are avoided, the problem being reduced to one of solving a set of ordinary differential equations.

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