Numerical Methods Applied to Mathematical Problems

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Computational and Applied Mathematics".

Deadline for manuscript submissions: 10 May 2025 | Viewed by 745

Special Issue Editor


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Guest Editor
Department of Management Science and Technology, University of Patras, 26334 Patras, Greece
Interests: optimization of algorithms; numerical solution of ODEs; artificial neural networks

Special Issue Information

Dear Colleagues,

This Special Issue, entitled “Numerical Methods Applied to Mathematical Problems”, is currently accepting submissions from a diverse range of scientific fields. Numerical methods represent a distinct branch of mathematics that is focused on developing and employing algorithms to tackle mathematical problems.

Numerical techniques have naturally found application in a variety of fields such as engineering, physics, finance, biology, and beyond. Due to the ever-growing complexity of mathematical challenges across various disciplines, numerical methods offer practical solutions with which to analyze, model, and solve these problems computationally.

The scope of this Special Issue includes, but is not limited to, the following topics:

Numerical methods for ODEs and PDEs; numerical linear algebra; stochastic differential equations; numerical integration and differentiation; dynamical systems; interval analysis; error analysis; approximation theory; interpolation; optimization; and mathematical modelling.

The submission of papers that investigate the practical utilization of numerical methods in addressing real-world challenges in all scientific fields is warmly encouraged.

Dr. Dimitris F. Papadopoulos
Guest Editor

Manuscript Submission Information

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Keywords

  • computational mathematics
  • error analysis
  • interval analysis
  • numerical algorithms
  • numerical analysis
  • numerical methods
  • numerical stability
  • optimization
  • ordinary differential equations
  • partial differential equations

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Published Papers (1 paper)

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Research

13 pages, 998 KiB  
Article
A Parametric Six-Step Method for Second-Order IVPs with Oscillating Solutions
by Dimitris F. Papadopoulos
Mathematics 2024, 12(23), 3824; https://doi.org/10.3390/math12233824 - 3 Dec 2024
Viewed by 512
Abstract
In this paper, we develop an explicit symmetric six-step method for the numerical solution of second-order initial value problems (IVPs) with oscillating solutions. The proposed method is phase-fitted and incorporates a free coefficient as a parameter to optimize its performance. By exploring a [...] Read more.
In this paper, we develop an explicit symmetric six-step method for the numerical solution of second-order initial value problems (IVPs) with oscillating solutions. The proposed method is phase-fitted and incorporates a free coefficient as a parameter to optimize its performance. By exploring a wide range of values for this parameter, we computationally determine the periodicity interval. The objective of this procedure is to identify the range of the parameter’s values for which the method remains stable. Based on the output from the periodicity interval analysis, we then aim to define the optimal values for the parameter by numerically solving three initial value problems. The results guided us in identifying these optimal values and confirm the high efficiency of the new method. The method’s efficiency is further validated for the chosen optimal parameter value for specific oscillatory problems, where it is compared with well-known phase-fitted methods. Full article
(This article belongs to the Special Issue Numerical Methods Applied to Mathematical Problems)
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