Fundamental solutions to Helmholtz's equation for inhomogeneous media by a first-order differential equation system

1997 ◽  
Vol 16 (2) ◽  
pp. 81-94 ◽  
Author(s):  
George D. Manolis ◽  
Richard P. Shaw
Keyword(s):  
Differential Equation ◽  
Order Differential Equation ◽  
Equation System ◽  
Fundamental Solutions ◽  
Inhomogeneous Media ◽  
Differential Equation System ◽  
First Order

The Generation of a Series of Multiwing Chaotic Attractors Using Integer and Fractional Order Differential Equation Systems

2014 ◽  
Vol 24 (10) ◽  
pp. 1450130
Author(s):  
Fei Xu
Keyword(s):  
Differential Equation ◽  
Fractional Order ◽  
Systematic Approach ◽  
Order Differential Equation ◽  
Equation System ◽  
Chaotic Attractors ◽  
Differential Equation System ◽  
Fractional Order Differential Equation ◽  
Integer Order

In this article, we present a systematic approach to design chaos generators using integer order and fractional order differential equation systems. A series of multiwing chaotic attractors and grid multiwing chaotic attractors are obtained using linear integer order differential equation systems with switching controls. The existence of chaotic attractors in the corresponding fractional order differential equation systems is also investigated. We show that, using the nonlinear fractional order differential equation system, or linear fractional order differential equation systems with switching controls, a series of multiwing chaotic attractors can be obtained.

scholarly journals Revitalisasi Danau Limboto dengan Pengerukan Endapan di Danau: Pemodelan, Analisis, dan Simulasinya

2020 ◽  
Vol 1 (1) ◽  
pp. 31-40
Author(s):  
Sri Lestari Mahmud ◽  
Novianita Achmad ◽  
Hasan S. Panigoro
Keyword(s):  
Water Hyacinth ◽  
Order Differential Equation ◽  
Equilibrium Points ◽  
Fish Farming ◽  
Equation System ◽  
Household Waste ◽  
Differential Equation System ◽  
First Order ◽  
Mathematical Symbols ◽  
The Stability

Limboto lake is one of assets of Province of Gorontalo that provides many benefits to the surrounding society. The main problem of Limboto lake is the silting of the lake due to sedimentation caused by forest erosion, household waste, water hyacinth, and fish farming which is not environmentally friendly. In this article, a mathematical approach is used to modeling the Limboto lake siltation by including the revitalization solution namely the lake dredging. Mathematical modeling begins by building and limiting assumptions, constructing variables and parameters in mathematical symbols, and forming them into a first order differential equation system deterministically. Furthermore, we study the dynamics of the model such as identifying the existence of equilibrium points and their stability conditions. We also give a numerical simulations to show the conditions based on the stability requirements in previous analytical results.

scholarly journals The Second-Order Differential Equation System with the Controlled Process for Variational Inequality with Constraints

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Li Wang ◽  
Xingxu Chen ◽  
Juhe Sun
Keyword(s):  
Differential Equation ◽  
Variational Inequality ◽  
Optimization Problem ◽  
Order Differential Equation ◽  
Lagrange Function ◽  
Equation System ◽  
Accumulation Point ◽  
Second Order ◽  
Differential Equation System ◽  
Second Order Differential Equation

In this paper, the variational inequality with constraints can be viewed as an optimization problem. Using Lagrange function and projection operator, the equivalent operator equations for the variational inequality with constraints under the certain conditions are obtained. Then, the second-order differential equation system with the controlled process is established for solving the variational inequality with constraints. We prove that any accumulation point of the trajectory of the second-order differential equation system is a solution to the variational inequality with constraints. In the end, one example with three kinds of different cases by using this differential equation system is solved. The numerical results are reported to verify the effectiveness of the second-order differential equation system with the controlled process for solving the variational inequality with constraints.

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