scholarly journals General solutions of the nonlinear PDEs governing the erosion kinetics

2002 ◽  
Vol 8 (1) ◽  
pp. 69-85
Author(s):  
D. E. Panayotounakos ◽  
K. P. Zafeiropoulos
Keyword(s):  
Partial Differential Equations ◽  
General Solution ◽  
Initial Conditions ◽  
Nonlinear Partial Differential Equations ◽  
Nonlinear Pde ◽  
Nonlinear Pdes ◽  
General Solutions ◽  
One Dimensional ◽  
Full Complement ◽  
The One

We present the construction of the general solutions concerning the one-dimensional (1D) fully dynamic nonlinear partial differential equations (PDEs), for the erosion kinetics. After an uncoupling procedure of the above mentioned equations a second–order nonlinear PDE of the Monge type governing the porosity is derived, the general solution of which is constructed in the sense that a full complement of arbitrary functions (as many as the order) is introduced. Afterwards, we specify the above solution according to convenient initial conditions.

scholarly journals On sound waves of finite amplitude

1953 ◽  
Vol 216 (1127) ◽  
pp. 539-547 ◽  
Keyword(s):  
Integral Equation ◽  
Analytical Solution ◽  
Arbitrary Function ◽  
Initial Conditions ◽  
Finite Amplitude ◽  
Sound Waves ◽  
One Dimensional ◽  
The One ◽  
Complex Integral ◽  
Gas Cloud

An analytical solution of Riemann’s equations for the one-dimensional propagation of sound waves of finite amplitude in a gas obeying the adiabatic law p = k ρ γ is obtained for any value of the parameter γ. The solution is in the form of a complex integral involving an arbitrary function which is found from the initial conditions by solving a generalization of Abel’s integral equation. The results are applied to the problem of the expansion of a gas cloud into a vacuum.

A MATHEMATICAL MODEL FOR THE REPRODUCTION DYNAMICS OF TOXOPLASMA GONDII

2015 ◽  
Vol 23 (supp01) ◽  
pp. S91-S100
Author(s):  
JOHN ALEXANDER LEÓN MARÍN ◽  
IRENE DUARTE GANDICA
Keyword(s):  
Mathematical Model ◽  
Partial Differential Equations ◽  
Toxoplasma Gondii ◽  
Epithelial Cells ◽  
Sexual Reproduction ◽  
Numerical Solution ◽  
Definitive Host ◽  
Initial Conditions ◽  
Felis Catus ◽  
One Dimensional

This paper presents a mathematical model describing the reproduction dynamics of the Toxoplasma gondii parasite in the definitive host Felis catus (cat). The dynamics is described by a system of partial differential equations defined in a one-dimensional region, with boundary and initial conditions. The model considers both asexual and sexual reproduction processes of the T. gondii parasite starting from the consumption of T. gondii oocysts from the environment, by the definitive host, and describing the reproduction dynamics until the cat expels infectious oocysts to the environment through its feces. The numerical solution of the system is obtained, and some simulations are made, leaving constant of transition and loss rates, since its variation does not produce significant changes in the reproduction, propagation and creation of new populations; and varying the initial consumption of oocysts from the environment by the cat. It is concluded that, either low or high, the involved populations are always reproduced; they spread by all over epithelial cells and subsequently are expelled to the environment through the cat feces. It is corroborated that the cats are potential multipliers of the oocysts and therefore, the main disseminators of the infection.

scholarly journals The homogeneous balance of undetermined coefficients method and its application

2016 ◽  
Vol 14 (1) ◽  
pp. 816-826 ◽  
Author(s):  
Yi Wei ◽  
Xin-Dang He ◽  
Xiao-Feng Yang
Keyword(s):  
Partial Differential Equations ◽  
Boussinesq Equation ◽  
Kdv Equation ◽  
Nonlinear Partial Differential Equations ◽  
Nonlinear Pdes ◽  
The Kdv Equation ◽  
Generalized Boussinesq Equation ◽  
Positive Integers ◽  
Bilinear Equation ◽  
Homogeneous Balance

AbstractThe homogeneous balance of undetermined coefficients method is firstly proposed to solve such nonlinear partial differential equations (PDEs), the balance numbers of which are not positive integers. The proposed method can also be used to derive more general bilinear equation of nonlinear PDEs. The Eckhaus equation, the KdV equation and the generalized Boussinesq equation are chosen to illustrate the validity of our method. The proposed method is also a standard and computable method, which can be generalized to deal with some types of nonlinear PDEs.

scholarly journals Application of Conformable Sumudu Decomposition Method for Solving Conformable Fractional Coupled Burger’s Equation

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Hassan Eltayeb ◽  
Said Mesloub
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Analytical Method ◽  
Decomposition Method ◽  
Nonlinear Partial Differential Equations ◽  
One Dimensional ◽  
Burger's Equation ◽  
Burger’S Equation ◽  
Sumudu Transform ◽  
Linear And Nonlinear

The conformable double Sumudu decomposition method (CDSDM) is a combination of decomposition method (DM) and a conformable double Sumudu transform. It is an approximate analytical method, which can be used to solve linear and nonlinear partial differential equations. In this work, one-dimensional conformable functional Burger’s equation has been solved by applying conformable double Sumudu decomposition. Two examples are used to illustrate the method.

High Pressure Diesel Engine Modeling

2003 ◽  
Author(s):  
Riccardo Baudille ◽  
Gino Bella ◽  
Rossella Rotondi
Keyword(s):  
Liquid Fuel ◽  
Initial Conditions ◽  
Injection Velocity ◽  
Dimensional Model ◽  
Flow Conditions ◽  
One Dimensional ◽  
Engine Modeling ◽  
Fuel Jet ◽  
Initial Drop ◽  
The One

In multi hole Diesel injectors, cavitation can offer advantages in the development on the fuel spray, because the primary atomization of the liquid fuel jet can be improved due to the enhanced turbulence. Several multi dimensional models of cavitating nozzle flow have been developed in order to provide information about the flow at the exit of a cavitating orifice. In this paper an analytical one-dimensional model, by Sarre et al. [1], to predict the flow conditions at the exit of a cavitating nozzle, is analyzed. The results obtained are compared with the ones obtained using the multi dimensional code Fluent in order to investigate the predictive capability of the one-dimensional code. The model provides initial conditions for multidimensional spray modeling: the effective injection velocity and the initial drop or injected liquid ‘blob’ size. The simulations were performed using an improved version of the KIVA3V code, in which an hybrid break up model, developed by the authors, is used and the results in terms of penetrations and global SMD are compared with the experimental ones. The one dimensional model predicts reasonable discharge coefficient for sharp injector geometry. Where the r/d ratio increases and the cavitation effects appear not clearly marked there are same discrepancies between the one dimensional and the multidimensional approach.

Analyzing Devaney Chaos of a Sine–Cosine Compound Function System

2018 ◽  
Vol 28 (14) ◽  
pp. 1850176 ◽  
Author(s):  
Hegui Zhu ◽  
Wentao Qi ◽  
Jiangxia Ge ◽  
Yuelin Liu
Keyword(s):  
Chaotic Behavior ◽  
Initial Conditions ◽  
Function System ◽  
Topological Transitivity ◽  
One Dimensional ◽  
Devaney’S Chaos ◽  
Chebyshev Map ◽  
Sensitive Dependence ◽  
Sine Map ◽  
The One

The one-dimensional Sine map and Chebyshev map are classical chaotic maps, which have clear chaotic characteristics. In this paper, we establish a chaotic framework based on a Sine–Cosine compound function system by analyzing the existing one-dimensional Sine map and Chebyshev map. The sensitive dependence on initial conditions, topological transitivity and periodic-point density of this chaotic framework is proved, showing that the chaotic framework satisfies Devaney’s chaos definition. In order to illustrate the chaotic behavior of the chaotic framework, we propose three examples, called Cosine–Polynomial (C–P) map, Sine–Tangent (S–T) map and Sine–Exponent (S–E) map, respectively. Then, we evaluate the chaotic behavior with Sine map and Chebyshev map by analyzing bifurcation diagrams, Lyapunov exponents, correlation dimensions, Kolmogorov entropy and [Formula: see text] complexity. Experimental results show that the chaotic framework has better unpredictability and more complex chaotic behaviors than the classical Sine map and Chebyshev map. The results also verify the effectiveness of the theoretical analysis of the proposed chaotic framework.

scholarly journals Exact solutions of the Biswas-Milovic equation, the ZK(m,n,k) equation and the K(m,n) equation using the generalized Kudryashov method

Open Physics ◽  
2016 ◽  
Vol 14 (1) ◽  
pp. 129-139 ◽  
Author(s):  
EL Sayed M.E. Zayed ◽  
Abdul-Ghani Al-Nowehy
Keyword(s):  
Partial Differential Equations ◽  
Exact Solutions ◽  
Power Law ◽  
Nonlinear Partial Differential Equations ◽  
Nonlinear Pdes ◽  
Hyperbolic Function ◽  
Generalized Kudryashov Method ◽  
Kudryashov Method ◽  
Hyperbolic Function Solutions ◽  
Fibonacci Function

AbstractIn this article, we apply the generalized Kudryashov method for finding exact solutions of three nonlinear partial differential equations (PDEs), namely: the Biswas-Milovic equation with dual-power law nonlinearity; the Zakharov--Kuznetsov equation (ZK(m,n,k)); and the K(m,n) equation with the generalized evolution term. As a result, many analytical exact solutions are obtained including symmetrical Fibonacci function solutions, and hyperbolic function solutions. Physical explanations for certain solutions of the three nonlinear PDEs are obtained.

scholarly journals Solutions of Smooth Nonlinear Partial Differential Equations

2011 ◽  
Vol 2011 ◽  
pp. 1-37
Author(s):  
Jan Harm van der Walt
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Nonlinear Partial Differential Equations ◽  
Spatial Dimension ◽  
Nonlinear Pdes ◽  
Generalized Solutions ◽  
Structure Of Solutions ◽  
Partial Differential ◽  
Convergence Spaces ◽  
Order Completion

The method of order completion provides a general and type-independent theory for the existence and basic regularity of the solutions of large classes of systems of nonlinear partial differential equations (PDEs). Recently, the application of convergence spaces to this theory resulted in a significant improvement upon the regularity of the solutions and provided new insight into the structure of solutions. In this paper, we show how this method may be adapted so as to allow for the infinite differentiability of generalized functions. Moreover, it is shown that a large class of smooth nonlinear PDEs admit generalized solutions in the space constructed here. As an indication of how the general theory can be applied to particular nonlinear equations, we construct generalized solutions of the parametrically driven, damped nonlinear Schrödinger equation in one spatial dimension.

scholarly journals Classification of Exact Solutions for Some Nonlinear Partial Differential Equations with Generalized Evolution

2012 ◽  
Vol 2012 ◽  
pp. 1-16 ◽  
Author(s):  
Yusuf Pandir ◽  
Yusuf Gurefe ◽  
Ugur Kadak ◽  
Emine Misirli
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Exact Solutions ◽  
Kdv Equation ◽  
Nonlinear Partial Differential Equations ◽  
Polynomial Method ◽  
Partial Differential ◽  
Elliptic Solutions ◽  
The One

We obtain the classification of exact solutions, including soliton, rational, and elliptic solutions, to the one-dimensional general improved Camassa Holm KP equation and KdV equation by the complete discrimination system for polynomial method. In discussion, we propose a more general trial equation method for nonlinear partial differential equations with generalized evolution.

Sign in / Sign up

Export Citation Format

Share Document