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Dr. Xiaofeng Wang

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School of Mathematical Sciences, Bohai University, Jinzhou 121013, China

Dr. Fazlollah Soleymani

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Institute for Advanced Studies in Basic Sciences, Zanjan, Iran

Fractal and Design of Multipoint Iterative Methods for Nonlinear Problems

Abstract submission deadline

30 April 2024

Manuscript submission deadline

30 June 2024

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6294

Topic Information

Dear Colleagues,

Solving nonlinear equations is an important problem in the areas of science and technology. The multipoint iterative method is a class of efficiency methods for solving nonlinear equations that can reach high convergence orders with less computational cost. In recent years, with the rapid development of computer technology, research on the multipoint iterative method has also developed rapidly. The main aim of this Special Issue is to show some research results of the multipoint iterative method. We welcome manuscripts that consider, but are not limited to, the following areas: Study of the stability of the multipoint iterative method by using complex and real dynamics; Fractional order multipoint iterative method for solving nonlinear equations; Design of Newton-type iterative method with and without memory; Design of Steffensen-type iterative method with and without memory; Application of the multipoint iterative method for solving matrix sign function; Application in ODEs/PDEs/SDEs.

Dr. Xiaofeng Wang
Dr. Fazlollah Soleymani
Topic Editors

Keywords

multipoint iterative method
nonlinear equations
dynamical analysis
basin of attractor
convergence order
iterative method for matrix sign function
with memory
Steffensen-type iterative method
Newton-type iterative method
computational efficiency

Participating Journals

Journal Name	Impact Factor	CiteScore	Launched Year	First Decision (median)	APC
Algorithms algorithms	2.3	3.7	2008	19.1 Days	CHF 1600	Submit
Axioms axioms	2.0	2.2	2012	20 Days	CHF 2400	Submit
Fractal and Fractional fractalfract	5.4	3.6	2017	19.8 Days	CHF 2700	Submit
Mathematics mathematics	2.4	3.5	2013	17.7 Days	CHF 2600	Submit
Symmetry symmetry	2.7	4.9	2009	14.7 Days	CHF 2400	Submit

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Published Papers (7 papers)

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Open AccessArticle

Global Classical Solutions of the 1.5D Relativistic Vlasov–Maxwell–Chern–Simons System

and

Axioms 2023, 12(7), 627; https://doi.org/10.3390/axioms12070627 - 25 Jun 2023

Viewed by 329

Abstract

We investigate the kinetic model of the relativistic Vlasov–Maxwell–Chern–Simons system, which originates from gauge theory. This system can be seen as an electromagnetic fields (i.e., Maxwell–Chern–Simons fields) perturbation for the classical Vlasov equation. By virtue of a nondecreasing function and an iteration method, [...] Read more.

(This article belongs to the Topic Fractal and Design of Multipoint Iterative Methods for Nonlinear Problems)

Open AccessArticle

A Fast Computational Scheme for Solving the Temporal-Fractional Black–Scholes Partial Differential Equation

and

Fractal Fract. 2023, 7(4), 323; https://doi.org/10.3390/fractalfract7040323 - 12 Apr 2023

Viewed by 867

Abstract

In this work, we propose a fast scheme based on higher order discretizations on graded meshes for resolving the temporal-fractional partial differential equation (PDE), which benefits the memory feature of fractional calculus. To avoid excessively increasing the number of discretization points, such as the standard finite difference or meshfree methods, and, at the same time, to increase the efficiency of the solver, we employ discretizations on spatially non-uniform meshes with an attention on the non-smoothness area of the underlying asset. Therefore, the PDE problem is transformed to a linear system of algebraic equations. We perform numerical simulations to observe and check the behavior of the presented scheme in contrast to the existing methods. Full article

(This article belongs to the Topic Fractal and Design of Multipoint Iterative Methods for Nonlinear Problems)

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Open AccessArticle

Stability Analysis of Simple Root Seeker for Nonlinear Equation

Xiaofeng Wang

and

Wenshuo Li

Axioms 2023, 12(2), 215; https://doi.org/10.3390/axioms12020215 - 18 Feb 2023

Cited by 3 | Viewed by 681

Abstract

In this paper, the stability of a class of Liu–Wang’s optimal eighth-order single-parameter iterative methods for solving simple roots of nonlinear equations was studied by applying them to arbitrary quadratic polynomials. Under the Riemann sphere and scaling theorem, the complex dynamic behavior of the iterative method was analyzed by fractals. We discuss the stability of all fixed points and the parameter spaces starting from the critical points with the Mathematica software. The dynamical planes of the elements with good and bad dynamical behavior are given, and the optimal parameter element with stable behavior was obtained. Finally, a numerical experiment and practical application were carried out to prove the conclusion. Full article

(This article belongs to the Topic Fractal and Design of Multipoint Iterative Methods for Nonlinear Problems)

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Open AccessArticle

From Fractal Behavior of Iteration Methods to an Efficient Solver for the Sign of a Matrix

Tao Liu

Malik Zaka Ullah

Khalid Mohammed Ali Alshahrani

and

Stanford Shateyi

Fractal Fract. 2023, 7(1), 32; https://doi.org/10.3390/fractalfract7010032 - 28 Dec 2022

Viewed by 711

Abstract

Investigating the fractal behavior of iteration methods on special polynomials can help to find iterative methods with global convergence for finding special matrix functions. By employing such a methodology, we propose a new solver for the sign of an invertible square matrix. The presented method achieves the fourth rate of convergence by using as few matrix products as possible. Its attraction basin shows larger convergence radii, in contrast to its Padé-type methods of the same order. Computational tests are performed to check the efficacy of the proposed solver. Full article

(This article belongs to the Topic Fractal and Design of Multipoint Iterative Methods for Nonlinear Problems)

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Open AccessArticle

Choosing the Best Members of the Optimal Eighth-Order Petković’s Family by Its Fractal Behavior

Xiaofeng Wang

and

Wenshuo Li

Fractal Fract. 2022, 6(12), 749; https://doi.org/10.3390/fractalfract6120749 - 19 Dec 2022

Cited by 2 | Viewed by 886

Abstract

In this paper, by applying Petković’s iterative method to the Möbius conjugate mapping of a quadratic polynomial function, we attain an optimal eighth-order rational operator with a single parameter r and research the stability of this method by using complex dynamics tools on the basis of fractal theory. Through analyzing the stability of the fixed point and drawing the parameter space related to the critical point, the parameter family which can make the behavior of the corresponding iterative method stable or unstable is obtained. Lastly, the consequence is verified by showing their corresponding dynamical planes. Full article

(This article belongs to the Topic Fractal and Design of Multipoint Iterative Methods for Nonlinear Problems)

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Open AccessArticle

Interactions of Logistic Distribution to Credit Valuation Adjustment: A Study on the Associated Expected Exposure and the Conditional Value at Risk

and

Mathematics 2022, 10(20), 3828; https://doi.org/10.3390/math10203828 - 17 Oct 2022

Cited by 1 | Viewed by 679

Abstract

In Basel III, the credit valuation adjustment (CVA) was given, and it was discussed that a bank covers mark-to-market losses for expected counterparty risk with a CVA capital charge. The purpose of this study is threefold. Using the logistic distribution, it is shown how the expected exposure can be derived for an interest rate swap. Secondly, the risk measure of VaR is contributed for the CVA under this distribution. Thirdly, generalizations for the CVA VaR and CVA CVaR are given by considering both the credit spread and the expected positive exposure to follow the logistic distributions with different parameters. Finally, several simulations are provided to uphold the theoretical discussions. Full article

(This article belongs to the Topic Fractal and Design of Multipoint Iterative Methods for Nonlinear Problems)

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Open AccessArticle

Inverse Multiquadric Function to Price Financial Options under the Fractional Black–Scholes Model

Yanlai Song

and

Stanford Shateyi

Fractal Fract. 2022, 6(10), 599; https://doi.org/10.3390/fractalfract6100599 - 15 Oct 2022

Cited by 4 | Viewed by 947

Abstract

The inverse multiquadric radial basis function (RBF), which is one of the most important functions in the theory of RBFs, is employed on an adaptive mesh of points for pricing a fractional Black–Scholes partial differential equation (PDE) based on the modified RL derivative. To solve this problem, discretization along space is carried out on a non-uniform grid in order to focus on the hot area, at which the initial condition of the pricing model, i.e., the payoff, has discontinuity. The L1 scheme having the convergence order

2 - α

is used along the time fractional variable. Then, our proposed numerical method is built by matrices of differentiations to be as efficient as possible. Computational pieces of evidence are brought forward to uphold the theoretical discussions and show how the presented method is efficient in contrast to the exiting solvers. Full article

(This article belongs to the Topic Fractal and Design of Multipoint Iterative Methods for Nonlinear Problems)

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Submit your Abstract

Journal Name	Impact Factor	CiteScore	Launched Year	First Decision (median)	APC
Algorithms algorithms	2.3	3.7	2008	19.1 Days	CHF 1600	Submit
Axioms axioms	2.0	2.2	2012	20 Days	CHF 2400	Submit
Fractal and Fractional fractalfract	5.4	3.6	2017	19.8 Days	CHF 2700	Submit
Mathematics mathematics	2.4	3.5	2013	17.7 Days	CHF 2600	Submit
Symmetry symmetry	2.7	4.9	2009	14.7 Days	CHF 2400	Submit

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Fractal and Design of Multipoint Iterative Methods for Nonlinear Problems

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Published Papers (7 papers)

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