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 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.

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 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.

scholarly journals Stable high-order iterative methods for solving nonlinear models

2017 ◽  
Vol 303 ◽  
pp. 70-88 ◽  
Author(s):  
Ramandeep Behl ◽  
Alicia Cordero ◽  
Sandile S. Motsa ◽  
Juan R. Torregrosa
Keyword(s):  
Iterative Methods ◽  
Nonlinear Models ◽  
High Order ◽  
High Order Iterative Methods

An Initial Guess Free Method for Least Squares Parameter Estimation in Nonlinear Models

2020 ◽  
Author(s):  
Guanglu Zhang ◽  
Douglas Allaire ◽  
Jonathan Cagan
Keyword(s):  
Parameter Estimation ◽  
Iterative Methods ◽  
Optimal Parameter ◽  
Nonlinear Models ◽  
Search Space ◽  
Uncertainty Assessment ◽  
Initial Guess ◽  
Data Set ◽  
Parameter Estimators

Abstract Fitting models to data is critical in many science and engineering fields. A major task in fitting models to data is to estimate the value of each parameter in a given model. Iterative methods, such as the Gauss-Newton method and the Levenberg-Marquardt method, are often employed for parameter estimation in nonlinear models. However, practitioners must guess the initial value for each parameter in order to initialize these iterative methods. A poor initial guess can contribute to non-convergence of these methods or lead these methods to converge to a wrong solution. In this paper, an initial guess free method is introduced to find the optimal parameter estimators in a nonlinear model that minimizes the squared error of the fit. The method includes three algorithms that require different level of computational power to find the optimal parameter estimators. The method constructs a solution interval for each parameter in the model. These solution intervals significantly reduce the search space for optimal parameter estimators. The method also provides an empirical probability distribution for each parameter, which is valuable for parameter uncertainty assessment. The initial guess free method is validated through a case study in which Fick’s second law is fit to an experimental data set. This case study shows that the initial guess free method can find the optimal parameter estimators efficiently. A four-step procedure for implementing the initial guess free method in practice is also outlined.

Highly efficient and selective photocatalytic CO2 to CO conversion in aqueous solution

2020 ◽  
Vol 56 (27) ◽  
pp. 3851-3854 ◽  
Author(s):  
Xiaomin Chai ◽  
Hai-Hua Huang ◽  
Huiping Liu ◽  
Zhuofeng Ke ◽  
Wen-Wen Yong ◽  
...  
Keyword(s):  
Aqueous Solution ◽  
Photocatalytic Performance ◽  
Aqueous Media ◽  
Highly Efficient ◽  
Co Conversion

A Co-based complex displayed the highest photocatalytic performance for CO2 to CO conversion in aqueous media.

Tuning the pore structures and photocatalytic properties of a 2D covalent organic framework with multi-branched photoactive moieties

Nanoscale ◽  
2020 ◽  
Vol 12 (30) ◽  
pp. 16136-16142
Author(s):  
Xuan Wang ◽  
Ming-Jie Dong ◽  
Chuan-De Wu
Keyword(s):  
Photocatalytic Properties ◽  
Effective Strategy ◽  
Covalent Organic Framework ◽  
Highly Efficient ◽  
Pore Structures ◽  
Local Connection ◽  
Organic Framework

An effective strategy to incorporate accessible metalloporphyrin photoactive sites into 2D COFs by establishing a 3D local connection for highly efficient photocatalysis was developed.

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