A New Method to Find the Base Functions for the Method of Directly Defining the Inverse Mapping (MDDiM)

2018 ◽  
Vol 09 (04) ◽  
pp. 1850008
Author(s):  
OPhir Nave
Keyword(s):  
Numerical Simulation ◽  
Nonlinear System ◽  
Analytical Solution ◽  
Differential Equations ◽  
Analytical Solutions ◽  
New Method ◽  
Fuel Spray ◽  
System Of Differential Equations ◽  
Inverse Mapping ◽  
Base Functions

In this paper, we apply a new algorithm called method of directly defining the inverse mapping (MDDiM) that was introduced by Liao for finding a semi-analytical solution to nonlinear system of differential equations. We apply this new method to the autoignition of a monodisperse fuel spray model. We use this technique for finding the base functions in the considered algorithm. Our results include a comparison between a numerical simulation and an analytical solutions derived from the MDDiM.

Strongly Nonlinear Vibrations of a Hyperelastic Thin-walled Cylindrical Shell Based on the Modified Lindstedt–Poincaré Method

2019 ◽  
Vol 19 (12) ◽  
pp. 1950160 ◽  
Author(s):  
Jing Zhang ◽  
Jie Xu ◽  
Xuegang Yuan ◽  
Wenzheng Zhang ◽  
Datian Niu
Keyword(s):  
Cylindrical Shell ◽  
Nonlinear System ◽  
Differential Equations ◽  
Nonlinear Vibrations ◽  
Harmonic Excitation ◽  
System Of Differential Equations ◽  
Response Curves ◽  
Strongly Nonlinear ◽  
Hardening Behavior ◽  
Thin Walled

Some significant behaviors on strongly nonlinear vibrations are examined for a thin-walled cylindrical shell composed of the classical incompressible Mooney–Rivlin material and subjected to a single radial harmonic excitation at the inner surface. First, with the aid of Donnell’s nonlinear shallow-shell theory, Lagrange’s equations and the assumption of small strains, a nonlinear system of differential equations for the large deflection vibration of a thin-walled shell is obtained. Second, based on the condensation method, the nonlinear system of differential equations is reduced to a strongly nonlinear Duffing equation with a large parameter. Finally, by the appropriate parameter transformation and modified Lindstedt–Poincar[Formula: see text] method, the response curves for the amplitude-frequency and phase-frequency relations are presented. Numerical results demonstrate that the geometrically nonlinear characteristic of the shell undergoing large vibrations shows a hardening behavior, while the nonlinearity of the hyperelastic material should weak the hardening behavior to some extent.

scholarly journals A Modified SIRD Model to Study the Evolution of the COVID-19 Pandemic in Spain

Symmetry ◽  
2021 ◽  
Vol 13 (4) ◽  
pp. 723
Author(s):  
Vicente Martínez
Keyword(s):  
Nonlinear System ◽  
Differential Equations ◽  
System Of Differential Equations ◽  
Short Term ◽  
Exponential Expansion ◽  
Harmful Effects

In this paper, we use an SIRD model to analyze the evolution of the COVID-19 pandemic in Spain, caused by a new virus called SARS-CoV-2 from the coronavirus family. This model is governed by a nonlinear system of differential equations that allows us to detect trends in the pandemic and make reliable predictions of the evolution of the infection in the short term. This work shows this evolution of the infection in various changing stages throughout the period of maximum alert in Spain. It also shows a quick adaptation of the parameters that define the disease in several stages. In addition, the model confirms the effectiveness of quarantine to avoid the exponential expansion of the pandemic and reduce the number of deaths. The analysis shows good short-term predictions using the SIRD model, which are useful to influence the evolution of the epidemic and thus carry out actions that help reduce its harmful effects.

scholarly journals Analytical Solution for Differential and Nonlinear Integral Equations via F ϖ e -Suzuki Contractions in Modified ϖ e -Metric-Like Spaces

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Hasanen A. Hammad ◽  
Manuel De la Sen ◽  
Hassen Aydi
Keyword(s):  
Fixed Point ◽  
Analytical Solution ◽  
Differential Equations ◽  
Integral Equations ◽  
Analytical Solutions ◽  
Nonlinear Integral Equations ◽  
New Space

The aim of this manuscript is to present a new space, namely, a modified ϖ e -metric-like space, and we establish some related fixed point results using extended F ϖ e -Suzuki and generalized F ϖ e -Suzuki contractions on the mentioned space. Here, we support our theoretical consequences in two ways: the first one consists of presenting illustrative examples and the second one consists of finding analytical solutions for some integral and differential equations in the context of the mentioned space.

scholarly journals Solution of Fractional Autonomous Ordinary Differential Equations

2021 ◽  
Author(s):  
Rami AlAhmad ◽  
Qusai AlAhmad ◽  
Ahmad Abdelhadi
Keyword(s):  
Analytical Solution ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Fractional Order ◽  
Analytical Solutions ◽  
Singular Kernel ◽  
Autonomous Differential Equations ◽  
Implicit Analytical Solution

Autonomous differential equations of fractional order and non-singular kernel are solved. While solutions can be obtained through numerical, graphical, or analytical solutions, we seek an implicit analytical solution.

scholarly journals A New Approximate Analytical Method for ODEs

2014 ◽  
Vol 10 (1) ◽  
pp. 19-30
Author(s):  
Hossein Aminikhah
Keyword(s):  
Exact Solution ◽  
Nonlinear System ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Analytical Method ◽  
New Method ◽  
Good Stability ◽  
Linear And Nonlinear ◽  
Stability And Accuracy ◽  
Theoretical Considerations

Abstract In this paper, we propose a new algorithm for solving ordinary differential equations. We show the superiority of this algorithm by applying the new method for some famous ODEs. Theoretical considerations are discussed. The first He's polynomials have used to reach the exact solution of these problems. This method which has good stability and accuracy properties is useful in deal with linear and nonlinear system of ordinary differential equations.

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