scholarly journals Determine of the wave equation in the task of electrical oscillations

2018 ◽  
Vol 184 ◽  
pp. 01023
Author(s):  
Gordana V. Jelić ◽  
Vladica Stanojević ◽  
Dragana Radosavljević
Keyword(s):  
Wave Equation ◽  
Initial Conditions ◽  
Mathematical Physics ◽  
Equation Of Motion ◽  
Independent Variables ◽  
Equations Of Mathematical Physics ◽  
Basic Equations ◽  
Derivatives Of ◽  
Two Independent Variables ◽  
Transverse Oscillations

One of the basic equations of mathematical physics (for instance function of two independent variables) is the differential equation with partial derivatives of the second order (3). This equation is called the wave equation, and is provided when considering the process of transverse oscillations of wire, longitudinal oscillations of rod, electrical oscillations in a conductor, torsional vibration at waves, etc… The paper shows how to form the equation (3) which is the equation of motion of each point of wire with abscissa x in time t during its oscillation. It is also shown how to determine the equation (3) in the task of electrical oscillations in a conductor. Then equation (3) is determined, and this solution satisfies the boundary and initial conditions.

scholarly journals Local Fractional Variational Iteration Method for Local Fractional Poisson Equations in Two Independent Variables

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Li Chen ◽  
Yang Zhao ◽  
Hossein Jafari ◽  
J. A. Tenreiro Machado ◽  
Xiao-Jun Yang
Keyword(s):  
Iteration Method ◽  
Fractional Derivatives ◽  
Variational Iteration Method ◽  
Approximate Solutions ◽  
Mathematical Physics ◽  
Nondifferentiable Functions ◽  
Independent Variables ◽  
Poisson Equations ◽  
Variational Iteration ◽  
Two Independent Variables

The local fractional Poisson equations in two independent variables that appear in mathematical physics involving the local fractional derivatives are investigated in this paper. The approximate solutions with the nondifferentiable functions are obtained by using the local fractional variational iteration method.

scholarly journals New Hermite-Hadamard type inequalities for m and (α, m)-convex functions on the coordinates via generalized fractional integrals

2021 ◽  
Vol 40 (6) ◽  
pp. 1449-1472
Author(s):  
Seth Kermausuor
Keyword(s):  
Convex Functions ◽  
Type Inequality ◽  
Second Order ◽  
Fractional Integrals ◽  
Absolute Value ◽  
Partial Derivatives ◽  
Independent Variables ◽  
Functions Of Two Variables ◽  
Derivatives Of ◽  
Two Independent Variables

In this paper, we obtained a new Hermite-Hadamard type inequality for functions of two independent variables that are m-convex on the coordinates via some generalized Katugampola type fractional integrals. We also established a new identity involving the second order mixed partial derivatives of functions of two independent variables via the generalized Katugampola fractional integrals. Using the identity, we established some new Hermite-Hadamard type inequalities for functions whose second order mixed partial derivatives in absolute value at some powers are (α, m)-convex on the coordinates. Our results are extensions of some earlier results in the literature for functions of two variables.

Analogical Modelling and Numerical Simulation of the Adsorption Process for Poly-Phenothiazine Formaldehyde on Graphite Electrodes

2010 ◽  
Vol 7 (1) ◽  
Author(s):  
Mihaela-Ligia M. Unguresan ◽  
Delia Maria Gligor ◽  
Francisc Dulf ◽  
Tiberiu Colosi
Keyword(s):  
Numerical Simulation ◽  
Taylor Series ◽  
Adsorption Process ◽  
Phenothiazine Derivative ◽  
Graphite Electrodes ◽  
Partial Derivatives ◽  
Independent Variables ◽  
Regulation Scheme ◽  
Derivatives Of ◽  
Two Independent Variables

The paper presents the dispersion of the concentration y(t, s) on the length (s) with respect to time (t), corresponding to the adsorption process of a phenothiazine derivative on graphite electrodes. The numerical simulation by equations with partial derivatives of the second order with two independent variables (t and s) (PDE II.2), based on (Mpdx) which associates with Taylor series was performed. Also, the adsorption process defined by PDE II.2 was included in a regulation scheme of concentration y(t, s) with multiple freedom levels. It insures good performances and a remarkable flexibility for extending the method in similar categories of applications.

scholarly journals Riemann's method and the characteristic value and cauchy problems for the damped wave equation

1969 ◽  
Vol 10 (2) ◽  
pp. 147-152
Author(s):  
Eutiquio C. Young
Keyword(s):  
Wave Equation ◽  
Higher Dimensions ◽  
Riemann Function ◽  
Cauchy Problems ◽  
Independent Variables ◽  
Characteristic Value ◽  
The Cauchy Problem ◽  
Hyperbolic Differential Equations ◽  
Two Independent Variables

Riemann's method for solving the Cauchy problem for hyperbolic differential equations in two independent variables has been extended in a number of papers [4], [5], [2] to the wave equation in space of higher dimensions. The method, which consists in the determination of a so-called Riemann function, hinges on the solution of a characteristic value problem. Accordingly, if Riemann's method is to be used in solving a characteristic value problem, one will have to consider another characteristic value problem and thus the process becomes circular. This difficulty was first overcome by Protter [7] in solving the characteristic value problem for the wave equation in three variables. There he employed a variation of Riemann's method developed by Martin [5]. Martin's result was later extended by Diaz and Martin [2] to the wave equation in an arbitrary number of variables. This made it possible to extend Protter's result to the wave equation in space of higher dimensions [8].

scholarly journals Derivation of Fundamental Solution of Heat Equation by using Symmetry Reduction

2020 ◽  
Vol 9 (5) ◽  
pp. 2239-2243
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Fundamental Solution ◽  
Heat Equation ◽  
Initial Conditions ◽  
Mathematical Physics ◽  
Heat Equations ◽  
Partial Differential ◽  
Partial Derivatives ◽  
Derivatives Of

The objective of this article is to present the fundamental solution of heat equation using symmetry of reduction which is associated with partial derivatives of heat equations through its initial conditions (ICs). To emphasize our main results, we also consider some important way of solving of partial differential equation. The main results of our paper are quite general in nature and yield a very large interesting fundamental solution of heat equation and it is used for problems of differential mathematics and mathematical physics special in the area of thermodynamics.

Fractal geometry: what is it, and what does it do?

1989 ◽  
Vol 423 (1864) ◽  
pp. 3-16 ◽  
Keyword(s):  
Fractal Geometry ◽  
Physical Theory ◽  
Mathematical Physics ◽  
Middle Ground ◽  
Practical Application ◽  
The Bible ◽  
Pure Mathematics ◽  
Equations Of Mathematical Physics ◽  
Basic Equations ◽  
Geometric Order

Fractal geometry is a workable geometric middle ground between the excessive geometric order of Euclid and the geometric chaos of general mathematics. It is based on a form of symmetry that had previously been underused, namely invariance under contraction or dilation. Fractal geometry is conveniently viewed as a language that has proven its value by its uses. Its uses in art and pure mathematics, being without ‘practical’ application, can be said to be poetic. Its uses in various areas of the study of materials and of other areas of engineering are examples of practical prose. Its uses in physical theory, especially in conjunction with the basic equations of mathematical physics, combine poetry and high prose. Several of the problems that fractal geometry tackles involve old mysteries, some of them already known to primitive man, others mentioned in the Bible, and others familiar to every landscape artist.

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