Numerical Analysis and Advanced Applications

A special issue of Axioms (ISSN 2075-1680). This special issue belongs to the section "Mathematical Analysis".

Deadline for manuscript submissions: closed (30 June 2023) | Viewed by 3154

Special Issue Editors


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Department of Mathematics and Statistics, Faculty of Applied Sciences and Technology, Universiti Tun Hussein Onn Malaysia Pagoh Campus, KM 1, Jalan Panchor, Muar Johor 84600, Malaysia
Interests: fractional calculus; numerical analysis; mathematical biology; mathematical physics

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Department of Mathematics, Moscow State University of Civil Engineering, Moscow 129337, Russia
Interests: spectral properties of non-self-adjoint operators; evolution equations in the abstract Hilbert space; abstract fractional calculus; operator equations in Banach spaces; mapping theorems for operators acting in Banach spaces

Special Issue Information

Dear Colleagues,

This Special Issue aims to consider original papers in all fields of classical and modern analysis, with a focus on work that addresses significant problems in pure and applied nonlinear analysis. The main focus of this issue on “Applied Numerical Analysis” is the advance and dissemination of mathematical knowledge through high-quality papers that describe and analyze different fields of analysis, as well as their applications. The aim of this Special Issue is to publish the best research articles related to applied analysis within the scope, boosting cooperation with applications in other areas of mathematics, physics, biology, engineering, and economics. The Special Issue covers all areas of classical and modern mathematical analysis, including boundary value problems, differential equations and inclusions, function spaces, operator theory, approximations and expansions, calculus of variations and optimal control, dynamic systems, difference and functional equations, convex, functional and harmonic analysis, measure and integration, special functions, function theory in one and several variables and on infinite dimensional spaces, topological and metric spaces, numerical analysis, the  theory of non-self-adjoint operators, the theory of the  abstract evolution equations  as well as their applications.  Current research results containing new and significant ideas, as well as selected high-quality survey articles, are expected to appear.

Dr. Chang Phang
Dr. Maksim Kukushkin
Guest Editors

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Keywords

  • application of numerical analysis in engineering and sciences
  • numerical methods for ODEs, PDEs, FDEs
  • numerical differentiation and integration
  • approximate theory
  • stability and convergence of numerical methods
  • numerical methods for evolution equations in the abstract hilbert space

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Published Papers (2 papers)

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Research

15 pages, 565 KiB  
Article
An Efficient Jarratt-Type Iterative Method for Solving Nonlinear Global Positioning System Problems
by Saima Yaseen, Fiza Zafar and Hamed H. Alsulami
Axioms 2023, 12(6), 562; https://doi.org/10.3390/axioms12060562 - 7 Jun 2023
Cited by 3 | Viewed by 1245
Abstract
The global positioning system (GPS) is a satellite navigation system that determines locations. Whenever the baseline satellites are serviced or deactivated, the Space Force often flies more than 24 GPS satellites to maintain coverage. The additional satellites are not regarded as a part [...] Read more.
The global positioning system (GPS) is a satellite navigation system that determines locations. Whenever the baseline satellites are serviced or deactivated, the Space Force often flies more than 24 GPS satellites to maintain coverage. The additional satellites are not regarded as a part of the core constellation but may improve the performance of the GPS. In this study of GPS models, we solved various problems. We examined each set of four satellites separately. Advancements in computer softwares have made computations much more precise. We can use iterative methods to solve GPS problems. Iterative schemes for solving nonlinear equations have always been of great importance because of their applicability to real-world problems. This paper involves the development of an efficient family of sixth-order Jarratt-type iterative schemes for analyzing nonlinear global positioning systems. Full article
(This article belongs to the Special Issue Numerical Analysis and Advanced Applications)
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15 pages, 384 KiB  
Article
New Algorithms for Dealing with Fractional Initial Value Problems
by Iqbal M. Batiha, Ahmad A. Abubaker, Iqbal H. Jebril, Suha B. Al-Shaikh and Khaled Matarneh
Axioms 2023, 12(5), 488; https://doi.org/10.3390/axioms12050488 - 18 May 2023
Cited by 8 | Viewed by 1247
Abstract
This work purposes to establish two small numerical modifications for the Fractional Euler method (FEM) and the Modified Fractional Euler Method (MFEM) to deal with fractional initial value problems. Two such modifications, which are named Improved Modified Fractional Euler Method 1 (IMFEM 1) [...] Read more.
This work purposes to establish two small numerical modifications for the Fractional Euler method (FEM) and the Modified Fractional Euler Method (MFEM) to deal with fractional initial value problems. Two such modifications, which are named Improved Modified Fractional Euler Method 1 (IMFEM 1) and Improved Modified Fractional Euler Method 2 (IMFEM 2), endeavor to further enhance FEM and MFEM in terms of attaining more accuracy. By utilizing certain theoretical results, the resultant error bounds of the proposed methods are analyzed and estimated. Several numerical comparisons are carried out to validate the efficiency of our proposed methods. Full article
(This article belongs to the Special Issue Numerical Analysis and Advanced Applications)
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