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1
artículo
Publicado 2018
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In the present work, we study a non-homogeneous second order partial hyperbolic differential equation, its canonical form, its resolution using D’Alembert’s formula and Green’s theorem. Only mixed initial conditions that are not homogeneous are required to solve this problem. There are several physical problems that lead to this type of mathematical model, so this technique of resolution contributes to the knowledge of finding explicit solutions of problems such as two-dimensional wave type. Within the results the explicit solution of three cases is generated: regarding the homogeneity and non-homogeneity of the initial conditions and the term source, from the point of view of analytical solution for continuous functions.
2
artículo
Publicado 2018
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In the present work, we study a non-homogeneous second order partial hyperbolic differential equation, its canonical form, its resolution using D’Alembert’s formula and Green’s theorem. Only mixed initial conditions that are not homogeneous are required to solve this problem. There are several physical problems that lead to this type of mathematical model, so this technique of resolution contributes to the knowledge of finding explicit solutions of problems such as two-dimensional wave type. Within the results the explicit solution of three cases is generated: regarding the homogeneity and non-homogeneity of the initial conditions and the term source, from the point of view of analytical solution for continuous functions.
3
artículo
Publicado 2017
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In the present work, we study a non-homogeneous second-order partial hyperbolic differential equation, its canonical form, its resolution using D’Alembert’s formula and Green’s theorem. Only mixed initial conditions that are not homogeneous are required to solve this problem. There are several physical problems that lead to this type of mathematical model, so this technique of resolution contributes to the knowledge of finding explicit solutions of problems such as two-dimensional wave type. Within the results the explicit solution of three cases is generated:regarding the homogeneity and non-homogeneity of the initial conditions and the term source, from the point of view of analytical solution for continuous functions.
4
artículo
Publicado 2017
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In the present work, we study a non-homogeneous second-order partial hyperbolic differential equation, its canonical form, its resolution using D’Alembert’s formula and Green’s theorem. Only mixed initial conditions that are not homogeneous are required to solve this problem. There are several physical problems that lead to this type of mathematical model, so this technique of resolution contributes to the knowledge of finding explicit solutions of problems such as two-dimensional wave type. Within the results the explicit solution of three cases is generated:regarding the homogeneity and non-homogeneity of the initial conditions and the term source, from the point of view of analytical solution for continuous functions.
5
artículo
Publicado 2022
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This paper deals with stability of solution for a one-dimensional model of Rao–Nakra sandwich beam with Kelvin–Voigt damping and time delay given by 1ℎ1 − 1ℎ1 − (− + + ) − − ( ・ , − ) = 0, 3ℎ3 − 3ℎ3 + (− + + ) − = 0, ℎ + − (− + + ) − = 0. A sandwich beam is an engineering model that consists of three layers: two stiff outer layers, bottom and top faces, and a more compliant inner layer called “core layer”. Rao–Nakra system consists of three layers and the assumption is that there is no slip at the interface between contacts. The top and bottom layers are wave equations for the longitudinal displacements under Euler–Bernoulli beam assumptions. The core layer is one equation that describes the transverse displacement under Timoshenko beam assumptions. By using the semigroup theory, the well-posedness is given by applying the Lumer–Phillips ...
6
artículo
Publicado 2019
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Explicit Finite Diferences Methods (FDM) are used for numerical simulations in seismic problems. In these cases the medium is heterogeneous and for the guarantee of a precise and stable solution there is the need to use refined discretizations for spatial and temporal variables, resulting in large-scale problems. In this paper we present the explicit FDM for the wave equation in a heterogeneous domain and show the results through computer simulations.
7
artículo
Publicado 2019
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Explicit Finite Diferences Methods (FDM) are used for numerical simulations in seismic problems. In these cases the medium is heterogeneous and for the guarantee of a precise and stable solution there is the need to use refined discretizations for spatial and temporal variables, resulting in large-scale problems. In this paper we present the explicit FDM for the wave equation in a heterogeneous domain and show the results through computer simulations.
8
artículo
The present article has as a goal to show an alternative way for deriving the Black-Scholes equation using the Schrödinger equation of quantum mechanics, taking into account that both of these partial differential equations are quite similar.
9
artículo
Publicado 2024
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In the present work, the spectral differentiation method was studied to solve the scalar Burger’s partial differential equation. This equation has been of considerable physical interest as it can be regarded as a simplified version of the Navier-Stokes equations. Through this study, the spectral differentiation method and its convergence were described; additionally, the mimetic method and the use of the MOLE library for numerically solving the scalar Burger’s equation were presented.
10
artículo
This work contains the numerical solution of the KdV equation using the Petrov-Galerkin-Wavelet method. The interesting thing is to be able to calculate Wavelet integrals, using Biorthogonal Wavelets, the properties of symmetry allow the calculations to be significantly reduced. Here we will apply concepts of functional analysis and the theory of distributions immersed in the calculation of the weak derivative or distributional derivative. To obtain graphically the numerical solution and the analytical solution of this equation very used in the part of the wave and communications technology, as well as in the reconstruction of images. Recently, wavelet methods are applied to the numerical solution of partial differential equations, pioneering works in this direction are those of Beylkin, Dahmen, Jaffard and Glowinski, among others.
11
artículo
This work contains the numerical solution of the KdV equation using the Petrov-Galerkin-Wavelet method. The interesting thing is to be able to calculate Wavelet integrals, using Biorthogonal Wavelets, the properties of symmetry allow the calculations to be significantly reduced. Here we will apply concepts of functional analysis and the theory of distributions immersed in the calculation of the weak derivative or distributional derivative. To obtain graphically the numerical solution and the analytical solution of this equation very used in the part of the wave and communications technology, as well as in the reconstruction of images. Recently, wavelet methods are applied to the numerical solution of partial differential equations, pioneering works in this direction are those of Beylkin, Dahmen, Jaffard and Glowinski, among others.
12
artículo
For the best performance and longer duration of devices or elements that participate in a mechanical energy transport system, they require an adequate lubrication process in the areas exposed to friction: bearings, gears, cylinder-piston, etc. This process is very important for the optimal functioning of the system, since it reduces repair costs and unscheduled failures. One of the frequent problems of poor lubrication is generated by the Cavitation phenomenon, for this reason it is important to study its effects under operating conditions. In the present work, the formulation and numerical simulation of Cavitation in bearings is carried out, considering the variation of the viscosity of the lubricant in relation to the pressure and the distribution space. In other works carried out on this phenomenon, it is mentioned how complex it would be to develop a numerical process in a two-dimens...
13
tesis de maestría
The optimal control in linear systems is a widely known problem that leads to the solution of one or two equations of Ricatti. However, in non-linear systems is required to obtain the solution of the Hamilton-Jacobi-Bellman equation (HJB) or variations, which consist of quadratic first order and partial differential equations, that are really difficult to solve. On the other hand, many non-linear dynamical systems can be represented as polynomial functions, where thanks to abstract algebra there are several techniques that facilitate the analysis and work with polynomials. This is where the sum-of-squares approach can be used as a sufficient condition to determine the positivity of a polynomial, a tool that is used in the search for suboptimal solutions of the HJB equation for the synthesis of a controller. The main objective of this thesis is the analysis, improvement and/or extension o...
14
tesis de maestría
The optimal control in linear systems is a widely known problem that leads to the solution of one or two equations of Ricatti. However, in non-linear systems is required to obtain the solution of the Hamilton-Jacobi-Bellman equation (HJB) or variations, which consist of quadratic first order and partial differential equations, that are really difficult to solve. On the other hand, many non-linear dynamical systems can be represented as polynomial functions, where thanks to abstract algebra there are several techniques that facilitate the analysis and work with polynomials. This is where the sum-of-squares approach can be used as a sufficient condition to determine the positivity of a polynomial, a tool that is used in the search for suboptimal solutions of the HJB equation for the synthesis of a controller. The main objective of this thesis is the analysis, improvement and/or extension o...
15
objeto de conferencia
The authors thank the National Council of Science,Technology and Technological Innovation (CONCYTEC)-Peru and Technical University of Cotopaxi for the partial funding of this work and Professor Angel H. Moreno for their contributions to this work
16
artículo
Publicado 2021
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A quasi-three-dimensional solution for the bending analysis of simply supported orthotropic piezoelectric shallow shell panels subjected to thermal, mechanical and electrical potential is introduced. The mechanical governing equations are derived in term of three-dimensional equilibrium relations and the classical Maxwell's equations. The trough-the-thickness temperature is modeled by the Fourier's heat conduction equation. The coupled partial differential equations are solved by Navier closed form solutions. The trough-the-thickness profile for electrical potential, temperature profile and displacements is obtained by using a quasi-exact method so-called the differential quadrature method (DQM). Chebyshev polynomials of the third kind are used as the basis functions and the grid thickness domain discretization for the DQM. The interlaminar conditions for transverse stresses, temperature...
17
tesis de maestría
Publicado 2018
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The present work deals with the modeling of the cyanobacteria blooms phenomenon from Lake Taihu in China by a 3D hydro-ecological model and the implementation of this model for the simulation. The model is composed of: (1) a model of the lake hydrodynamics in two di- mensions: we used the Shallow Water equations which are a particular case of Navier- Stokes equations, where the vertical dimension is neglected; (2) a Water Quality Model (WQM): we used the Water Quality Analysis Simulation Program(WASP) model in which are represented the reactions between ecological variables such as phytoplankton, oxygen, nitrogen and phosphorus, and the transport and diffusion of these substances by the fluid (in our case the water). For the numerical resolution of the partial differential equations involved, the finite volume method was used with a non-uniform triangular mesh of the lake. The Navier- St...
18
artículo
Publicado 2018
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The critical flow velocity for a horizontal clamped-clamped pipe conveying two-phase flow is investigated. The system is represented by a coupled fluid-structure fourth-order Partial Differential Equation (PDE). In the case of the multiphase flow, the no-slip homogeneous flow is adopted. The PDE is transformed to a set of first-order ODEs using both Galerkin and state-space methods. The final system of equations represents an eigenvalue problem, where the eigenvalues are the natural frequency of the system. Specialized software has been employed to solve it. Results of critical flow velocity of gas as a function of homogeneous void fraction (fraction of the transversal area occupied by the gas) are presented representing a velocity stability map. The later suggest that the critical flow velocity increases with increasing the homogeneous void fraction. © 2018 Begell House Inc.. All right...
19
artículo
Publicado 2012
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A framework for pricing Asian power options is developed when the underlying asset follows a jumpfraction process. The partial differential equation (PDE) in the fractional environment with jump is constructed for such option using general Itô’s lemma and self-financing dynamic strategy. With the boundary condition, an analytic formula for the option with geometric average starting at any time before maturity is derived by solving the PDE, and the option with arithmetic average is evaluated in Monte Carlo simulation using control variate technique with the help of the above analytic solution. Overwhelming numerical evidence indicates that the technique proposed is computationally efficient and dramatically improves the accuracy of the simulated price. Moreover, this study will pave a novel way to copy with the option contracts based on thinly-traded assets like oil, or currencies or i...
20
artículo
Publicado 2020
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In this paper, a three-dimensional numerical solution for the bending study of laminated composite doubly-curved shells is presented. The partial differential equations are solved analytically by the Navier summation for the midsurface variables; this method is only valid for shells with constant curvature where boundary conditions are considered simply supported. The partial differential equations present different coefficients, which depend on the thickness coordinates. A semi-analytical solution and the so-called Differential Quadrature Method are used to calculate an approximated derivative of a certain function by a weighted summation of the function evaluated in a certain grin domain. Each layer is discretized by a grid point distribution such as: Chebyshev-Gauss-Lobatto, Legendre, Ding and Uniform. As part of the formulation, the inter-laminar continuity conditions of displacement...
