scholarly journals Two efficient numerical methods for solving Rosenau-KdV-RLW equation

2020 ◽  
Vol 48 (1) ◽  
Author(s):  
Sibel Ӧzer ◽  
Keyword(s):  
Convergence Rates ◽  
Equation System ◽  
Splitting Methods ◽  
Differential Equation System ◽  
B Spline ◽  
Runge Kutta Method ◽  
Rlw Equation ◽  
Spline Finite Element ◽  
Time Splitting ◽  
The Stability

In this study, two efficient numerical schemes based on B-spline finite element method (FEM) and time-splitting methods for solving Rosenau-KdV-RLW equation are presented. In the first method, the equation is solved by cubic B-spline Galerkin FEM. For the second method, after splitting Rosenau-KdV-RLW equation in time, it is solved by Strang timesplitting technique using cubic B-spline Galerkin FEM. The differential equation system in the methods is solved by the fourth-order Runge-Kutta method. The stability analysis of the methods is performed. Both methods are applied to an example. The obtained numerical results are compared with some methods available in the literature via the error norms and , convergence rates, and mass and energy conservation constants. The present results are found to be consistent with the compared ones.

scholarly journals A MATHEMATIC MODEL OF TWO MUTUALLY INTERACTING SPECIES WITH MORTALITY RATE FOR THE SECOND SPECIES

2017 ◽  
Vol 3 (2) ◽  
pp. 21-25
Author(s):  
Annisa Rahayu ◽  
Yuni Yulida ◽  
Faisal Faisal
Keyword(s):  
Mortality Rate ◽  
Interaction Model ◽  
Mathematic Model ◽  
Equation System ◽  
Differential Equation System ◽  
Interacting Species ◽  
Stability Model ◽  
Species Population ◽  
The Stability ◽  
Type Of Stability

One of the interactions that occur withinthe ecosystem is the interaction of mutualism. Such mutualism interactions can be modeled into mathematical models. Reddy (2011) study suggests a model of two mutually interacting species that assumes that each species can live without its mutualism partner. In fact, not all mutual species survive without their mutualism pairs. If it is assumed that the second species lives without its mutualism partner, the first species, then the natural growth rate of the second species population will decrease (the mortality rate). The purpose of this research is to explain the model of two mutually interacting species with mortality rate for the second species, to determine the equilibrium point and the type of stability, and to simulate them with several parameters. This research was done by way of literature studies. The result of this research is the model of two mutually interacting species with mortality rate for second species modeled using Nonlinear Differential Equation System. In the model, it was obtained 3 (three) points of equilibrium, with each type and type of stability investigated. Next up from the stability, model simulations were done. Based on several simulations conducted can be seen the value of parameters and initial values affect the population growth of both species. The interaction model of two mutual species will be stable if the first species survive and the second species over time will be extinct.

scholarly journals Stability of Non-Hyperbolic Equilibrium Point for Polynomial System of Differential Equations

TEM Journal ◽  
2021 ◽  
pp. 1418-1422
Author(s):  
Vahidin Hadžiabdić ◽  
Midhat Mehuljić ◽  
Jasmin Bektešević
Keyword(s):  
Differential Equations ◽  
Equilibrium Point ◽  
Normal Forms ◽  
Polynomial System ◽  
Equation System ◽  
Differential Equation System ◽  
Nonlinear Part ◽  
The Stability ◽  
Hyperbolic Equilibrium ◽  
Hyperbolic Equilibrium Point

In this paper, a polynomial system of plane differential equations is observed. The stability of the non-hyperbolic equilibrium point was analyzed using normal forms. The nonlinear part of the differential equation system is simplified to the maximum. Two nonlinear transformations were used to simplify first the quadratic and then the cubic part of the system of equations.

scholarly journals The hunting cooperation of a predator under two prey's competition and fear-effect in the prey-predator fractional-order model

2022 ◽  
Vol 7 (4) ◽  
pp. 5463-5479
Author(s):  
Ali Yousef ◽  
◽  
Ashraf Adnan Thirthar ◽  
Abdesslem Larmani Alaoui ◽  
Prabir Panja ◽  
...  
Keyword(s):  
Fractional Order ◽  
Equation System ◽  
Order System ◽  
Differential Equation System ◽  
Order Model ◽  
Predator Prey ◽  
Fear Effect ◽  
Fractional Order Model ◽  
Prey Interaction ◽  
The Stability

<abstract><p>This paper investigates a fractional-order mathematical model of predator-prey interaction in the ecology considering the fear of the prey, which is generated in addition by competition of two prey species, to the predator that is in cooperation with its species to hunt the preys. At first, we show that the system has non-negative solutions. The existence and uniqueness of the established fractional-order differential equation system were proven using the Lipschitz Criteria. In applying the theory of Routh-Hurwitz Criteria, we determine the stability of the equilibria based on specific conditions. The discretization of the fractional-order system provides us information to show that the system undergoes Neimark-Sacker Bifurcation. In the end, a series of numerical simulations are conducted to verify the theoretical part of the study and authenticate the effect of fear and fractional order on our model's behavior.</p></abstract>

DYNAMICS OF A PARTICULAR LORENZ TYPE SYSTEM

2010 ◽  
Vol 21 (07) ◽  
pp. 973-982 ◽  
Author(s):  
GIORGIO E. TESTONI ◽  
PAULO C. RECH
Keyword(s):  
Equilibrium Points ◽  
Three Dimensional ◽  
Type System ◽  
Equation System ◽  
Largest Lyapunov Exponent ◽  
Differential Equation System ◽  
Order Ordinary Differential Equation ◽  
First Order ◽  
The Stability ◽  
The Right

In this paper we analytically and numerically investigate the dynamics of a nonlinear three-dimensional autonomous first-order ordinary differential equation system, obtained from paradigmatic Lorenz system by suppressing the y variable in the right-hand side of the second equation. The Routh–Hurwitz criterion is used to decide on the stability of the nontrivial equilibrium points of the system, as a function of the parameters. The dynamics of the system is numerically characterized by using diagrams that associate colors to largest Lyapunov exponent values in the parameter-space. Additionally, phase-space plots and bifurcation diagrams are used to characterize periodic and chaotic attractors.

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 On the Stability of Lung Parenchymal Lesions with Applications to Early Pneumothorax Diagnosis

2013 ◽  
Vol 2013 ◽  
pp. 1-12
Author(s):  
Archis R. Bhandarkar ◽  
Rohan Banerjee ◽  
Padmanabhan Seshaiyer
Keyword(s):  
Equation System ◽  
Finite Energy ◽  
Differential Equation System ◽  
Lung Collapse ◽  
Structure Interaction ◽  
Proposed Model ◽  
Scan Data ◽  
The Stability ◽  
Structural Instabilities ◽  
Lung Ct

Spontaneous pneumothorax, a prevalent medical challenge in most trauma cases, is a form of sudden lung collapse closely associated with risk factors such as lung cancer and emphysema. Our work seeks to explore and quantify the currently unknown pathological factors underlying lesion rupture in pneumothorax through biomechanical modeling. We hypothesized that lesion instability is closely associated with elastodynamic strain of the pleural membrane from pulsatile air flow and collagen-elastin dynamics. Based on the principles of continuum mechanics and fluid-structure interaction, our proposed model coupled isotropic tissue deformation with pressure from pulsatile air motion and the pleural fluid. Next, we derived mathematical instability criteria for our ordinary differential equation system and then translated these mathematical instabilities to physically relevant structural instabilities via the incorporation of a finite energy limiter. The introduction of novel biomechanical descriptions for collagen-elastin dynamics allowed us to demonstrate that changes in the protein structure can lead to a transition from stable to unstable domains in the material parameter space for a general lesion. This result allowed us to create a novel streamlined algorithm for detecting material instabilities in transient lung CT scan data via analyzing deformations in a local tissue boundary.

scholarly journals ANALISIS PERILAKU SOLUSI MODEL GERAK AYUNAN YANG DIPENGARUHI GAYA GESEKAN YANG BERBANDING LURUS DENGAN KECEPATAN SUDUT

2018 ◽  
Vol 4 (1) ◽  
Author(s):  
Lasker P Sinaga
Keyword(s):  
Differential Equation ◽  
Periodic Solution ◽  
Angular Velocity ◽  
Nonlinear Model ◽  
Critical Points ◽  
Equation System ◽  
Motion Model ◽  
Differential Equation System ◽  
Pendulum Motion ◽  
The Stability

ABSTRAKModel gerak ayunan yang dipengaruhi gaya gesekan yang berbanding lurus dengan kecepatan sudut merupakan suatu persamaan diferensial nonlinear. Model ini diubah menjadi sistem persamaan diferensial nonlinear yang lebih sederhana dan memiliki solusi bersifat periodik dengan titik kritis  dengan n bilangan bulat. Titik-titik kritis akan  stabil jika n adalah bilangan genap dan sebaliknya, tidak stabil jika n adalah bilangan ganjil. Bentuk kestabilan (simpul, pelana atau spiral) dari titik kritis bergantung pada nilai-nilai parameter model tersebut.Kata kunci: persamaan diferensial, sistem dinamik, gerak ayunan, titik kritis, kestabilan   ABSTRACTThe pendulum motion model influenced by friction force that is directly proportional to the angular velocity. This model is converted into a simpler nonlinear differential equation system and has a periodic solution with critical point  where n is an integer. The critical points will be stable if n is an even numbers and vice versa, will be unstable if n is an odd number. The stability form (node, saddle or spiral) of critical points depends on the value of the model’s parameter.Key words: differential equation, dynamic system, pendulum motion, critical points, stability

Stability Analysis of the Nanjung Water Diversion Twin Tunnels based on Convergence Measurement

2019 ◽  
Vol 1 (1) ◽  
pp. 49-60
Author(s):  
Simon Heru Prassetyo ◽  
Ganda Marihot Simangunsong ◽  
Ridho Kresna Wattimena ◽  
Made Astawa Rai ◽  
Irwandy Arif ◽  
...  
Keyword(s):  
Stability Analysis ◽  
Convergence Rate ◽  
Critical Strain ◽  
Convergence Rates ◽  
Strain Analysis ◽  
Water Diversion ◽  
Tunnel Face ◽  
Tunnel Stability ◽  
The Stability ◽  
Twin Tunnels

This paper focuses on the stability analysis of the Nanjung Water Diversion Twin Tunnels using convergence measurement. The Nanjung Tunnel is horseshoe-shaped in cross-section, 10.2 m x 9.2 m in dimension, and 230 m in length. The location of the tunnel is in Curug Jompong, Margaasih Subdistrict, Bandung. Convergence monitoring was done for 144 days between February 18 and July 11, 2019. The results of the convergence measurement were recorded and plotted into the curves of convergence vs. day and convergence vs. distance from tunnel face. From these plots, the continuity of the convergence and the convergence rate in the tunnel roof and wall were then analyzed. The convergence rates from each tunnel were also compared to empirical values to determine the level of tunnel stability. In general, the trend of convergence rate shows that the Nanjung Tunnel is stable without any indication of instability. Although there was a spike in the convergence rate at several STA in the measured span, that spike was not replicated by the convergence rate in the other measured spans and it was not continuous. The stability of the Nanjung Tunnel is also confirmed from the critical strain analysis, in which most of the STA measured have strain magnitudes located below the critical strain line and are less than 1%.

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