Topic Editors

Dr. Xiaofeng Wang
School of Mathematical Sciences, Bohai University, Jinzhou 121013, China
Dr. Fazlollah Soleymani
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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2350

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
- 3.3 2008 17.6 Days 1600 CHF Submit
Axioms
axioms
1.824 2.6 2012 17.8 Days 1600 CHF Submit
Fractal and Fractional
fractalfract
3.577 2.8 2017 18.3 Days 1800 CHF Submit
Mathematics
mathematics
2.592 2.9 2013 16.8 Days 2100 CHF Submit
Symmetry
symmetry
2.940 4.3 2009 14.2 Days 2000 CHF Submit

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Published Papers (4 papers)

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Article
From Fractal Behavior of Iteration Methods to an Efficient Solver for the Sign of a Matrix
Fractal Fract. 2023, 7(1), 32; https://doi.org/10.3390/fractalfract7010032 - 28 Dec 2022
Viewed by 334
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 [...] Read more.
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
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Article
Choosing the Best Members of the Optimal Eighth-Order Petković’s Family by Its Fractal Behavior
Fractal Fract. 2022, 6(12), 749; https://doi.org/10.3390/fractalfract6120749 - 19 Dec 2022
Viewed by 504
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 [...] Read more.
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
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Article
Interactions of Logistic Distribution to Credit Valuation Adjustment: A Study on the Associated Expected Exposure and the Conditional Value at Risk
Mathematics 2022, 10(20), 3828; https://doi.org/10.3390/math10203828 - 17 Oct 2022
Viewed by 347
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 [...] Read more.
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
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Article
Inverse Multiquadric Function to Price Financial Options under the Fractional Black–Scholes Model
Fractal Fract. 2022, 6(10), 599; https://doi.org/10.3390/fractalfract6100599 - 15 Oct 2022
Cited by 1 | Viewed by 451
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. [...] Read more.
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 2α 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
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