Stability analysis of a parametric family of iterative methods for solving nonlinear models

2016 ◽  
Vol 285 ◽  
pp. 26-40 ◽  
Author(s):  
Alicia Cordero ◽  
José M. Gutiérrez ◽  
Á. Alberto Magreñán ◽  
Juan R. Torregrosa
Keyword(s):  
Stability Analysis ◽  
Iterative Methods ◽  
Nonlinear Models ◽  
Parametric Family

scholarly journals Stability analysis of a parametric family of seventh-order iterative methods for solving nonlinear systems

2018 ◽  
Vol 323 ◽  
pp. 43-57 ◽  
Author(s):  
Abdolreza Amiri ◽  
Alicia Cordero ◽  
M. Taghi Darvishi ◽  
Juan R. Torregrosa
Keyword(s):  
Stability Analysis ◽  
Nonlinear Systems ◽  
Iterative Methods ◽  
Parametric Family ◽  
Seventh Order

scholarly journals Multidimensional stability analysis of a family of biparametric iterative methods: CMMSE2016

2017 ◽  
Vol 55 (7) ◽  
pp. 1461-1480 ◽  
Author(s):  
Alicia Cordero ◽  
Javier G. Maimó ◽  
Juan R. Torregrosa ◽  
María P. Vassileva
Keyword(s):  
Stability Analysis ◽  
Iterative Methods

Highly efficient family of iterative methods for solving nonlinear models

2019 ◽  
Vol 346 ◽  
pp. 110-132 ◽  
Author(s):  
Ramandeep Behl ◽  
Í. Sarría ◽  
R. González ◽  
Á.A. Magreñán
Keyword(s):  
Iterative Methods ◽  
Nonlinear Models ◽  
Highly Efficient

scholarly journals Oscillatory behavior of two nonlinear microbial models of soil carbon decomposition

2014 ◽  
Vol 11 (7) ◽  
pp. 1817-1831 ◽  
Author(s):  
Y. P. Wang ◽  
B. C. Chen ◽  
W. R. Wieder ◽  
M. Leite ◽  
B. E. Medlyn ◽  
...  
Keyword(s):  
Stability Analysis ◽  
Microbial Biomass ◽  
Soil Carbon ◽  
Nonlinear Model ◽  
Linear Models ◽  
Nonlinear Models ◽  
Oscillatory Behavior ◽  
Carbon Pools ◽  
Carbon Decomposition ◽  
Pool Model

Abstract. A number of nonlinear models have recently been proposed for simulating soil carbon decomposition. Their predictions of soil carbon responses to fresh litter input and warming differ significantly from conventional linear models. Using both stability analysis and numerical simulations, we showed that two of those nonlinear models (a two-pool model and a three-pool model) exhibit damped oscillatory responses to small perturbations. Stability analysis showed the frequency of oscillation is proportional to √(ϵ−1−1) Ks/Vs in the two-pool model, and to √(ϵ−1−1) Kl/Vl in the three-pool model, where ϵ is microbial growth efficiency, Ks and Kl are the half saturation constants of soil and litter carbon, respectively, and /Vs and /Vl are the maximal rates of carbon decomposition per unit of microbial biomass for soil and litter carbon, respectively. For both models, the oscillation has a period of between 5 and 15 years depending on other parameter values, and has smaller amplitude at soil temperatures between 0 and 15 °C. In addition, the equilibrium pool sizes of litter or soil carbon are insensitive to carbon inputs in the nonlinear model, but are proportional to carbon input in the conventional linear model. Under warming, the microbial biomass and litter carbon pools simulated by the nonlinear models can increase or decrease, depending whether ϵ varies with temperature. In contrast, the conventional linear models always simulate a decrease in both microbial and litter carbon pools with warming. Based on the evidence available, we concluded that the oscillatory behavior and insensitivity of soil carbon to carbon input are notable features in these nonlinear models that are somewhat unrealistic. We recommend that a better model for capturing the soil carbon dynamics over decadal to centennial timescales would combine the sensitivity of the conventional models to carbon influx with the flexible response to warming of the nonlinear model.

Stability analysis of nonlinear models via exact piecewise Takagi-Sugeno models

2014 ◽  
Vol 47 (3) ◽  
pp. 7970-7975 ◽  
Author(s):  
Temoatzin González ◽  
Miguel Bernal ◽  
Raymundo Márquez
Keyword(s):  
Stability Analysis ◽  
Nonlinear Models ◽  
Takagi Sugeno

scholarly journals New Family of Iterative Methods for Solving Nonlinear Models

2018 ◽  
Vol 2018 ◽  
pp. 1-12 ◽  
Author(s):  
Faisal Ali ◽  
Waqas Aslam ◽  
Kashif Ali ◽  
Muhammad Adnan Anwar ◽  
Akbar Nadeem
Keyword(s):  
Mathematical Models ◽  
Convergence Analysis ◽  
Iterative Methods ◽  
Nonlinear Models ◽  
Graphical Analysis ◽  
Governing Equations ◽  
Iterative Schemes ◽  
New Family ◽  
Special Cases ◽  
Improved Performance

We introduce a new family of iterative methods for solving mathematical models whose governing equations are nonlinear in nature. The new family gives several iterative schemes as special cases. We also give the convergence analysis of our proposed methods. In order to demonstrate the improved performance of newly developed methods, we consider some nonlinear equations along with two complex mathematical models. The graphical analysis for these models is also presented.

scholarly journals New Iterative Methods for Solving Nonlinear Problems with One and Several Unknowns

Mathematics ◽  
2018 ◽  
Vol 6 (12) ◽  
pp. 296 ◽  
Author(s):  
Ramandeep Behl ◽  
Alicia Cordero ◽  
Juan Torregrosa ◽  
Ali Alshomrani
Keyword(s):  
Iterative Methods ◽  
Nonlinear Models ◽  
Nonlinear Problems ◽  
Chemical Reactor ◽  
Parallel Plates ◽  
Fractional Conversion ◽  
Factor Effect ◽  
New Type ◽  
Residual Errors ◽  
Better Than

In this manuscript, a new type of study regarding the iterative methods for solving nonlinear models is presented. The goal of this work is to design a new fourth-order optimal family of two-step iterative schemes, with the flexibility through weight function/s or free parameter/s at both substeps, as well as small residual errors and asymptotic error constants. In addition, we generalize these schemes to nonlinear systems preserving the order of convergence. Regarding the applicability of the proposed techniques, we choose some real-world problems, namely chemical fractional conversion and the trajectory of an electron in the air gap between two parallel plates, in order to study the multi-factor effect, fractional conversion of species in a chemical reactor, Hammerstein integral equation, and a boundary value problem. Moreover, we find that our proposed schemes run better than or equal to the existing ones in the literature.

Analysis of the Chatter Instability in a Nonlinear Model for Drilling

2006 ◽  
Vol 1 (4) ◽  
pp. 294-306 ◽  
Author(s):  
Sue Ann Campbell ◽  
Emily Stone
Keyword(s):  
Stability Analysis ◽  
Hopf Bifurcation ◽  
Nonlinear Models ◽  
Stability Boundary ◽  
Vibration Modes ◽  
Loss Of Stability ◽  
Chatter Vibration ◽  
Cutting Depth ◽  
Stability And Bifurcation Analysis ◽  
The Stability

In this paper we present stability analysis of a non-linear model for chatter vibration in a drilling operation. The results build our previous work [Stone, E., and Askari, A., 2002, “Nonlinear Models of Chatter in Drilling Processes,” Dyn. Syst., 17(1), pp. 65–85 and Stone, E., and Campbell, S. A., 2004, “Stability and Bifurcation Analysis of a Nonlinear DDE Model for Drilling,” J. Nonlinear Sci., 14(1), pp. 27–57], where the model was developed and the nonlinear stability of the vibration modes as cutting width is varied was presented. Here we analyze the effect of varying cutting depth. We show that qualitatively different stability lobes are produced in this case. We analyze the criticality of the Hopf bifurcation associated with loss of stability and show that changes in criticality can occur along the stability boundary, resulting in extra periodic solutions.

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