Editorial Board Members’ Collection Series: Theory and Its Applications in Problems of Mathematical Physics and of Mathematical Chemistry

A topical collection in Foundations (ISSN 2673-9321). This collection belongs to the section "Mathematical Sciences".

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Editors

Topical Collection Information

Dear Colleagues,

An increasing amount of research interest has focused on the development of mathematical methods for application in problems in physics and chemistry. This series collection welcomes but is not limited to studies in the following branches: classical mechanics (including Lagrangian and Hamiltonian), partial differential equations (including variational calculus, Fourier analysis, potential theory, and vector analysis), quantum theory (theory of atomic spectra, quantum mechanics, Schrödinger operators), relativity and quantum relativistic theories (both special and general theories of relativity), statistical mechanics (including ergodic theory), chemical graph theory (including mathematical study of isomerism and the development of topological descriptors), structure–property relationships (including quantitative and nonlinear), chemical aspects of group theory (including applications in stereochemistry and quantum chemistry), molecular knot theory, and circuit topology.

Prof. Dr. Ioannis K. Argyros
Prof. Dr. Lorentz Jäntschi
Collection Editors

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Keywords

  • mathematical physics
  • mathematical chemistry
  • theoretical physics
  • theoretical chemistry
  • iterative methods
  • astrophysics
  • radiative transfer

Published Papers (1 paper)

2023

14 pages, 317 KiB  
Article
Extended Convergence of Two Multi-Step Iterative Methods
by Samundra Regmi, Ioannis K. Argyros, Jinny Ann John and Jayakumar Jayaraman
Foundations 2023, 3(1), 140-153; https://doi.org/10.3390/foundations3010013 - 13 Mar 2023
Cited by 1 | Viewed by 1019
Abstract
Iterative methods which have high convergence order are crucial in computational mathematics since the iterates produce sequences converging to the root of a non-linear equation. A plethora of applications in chemistry and physics require the solution of non-linear equations in abstract spaces iteratively. [...] Read more.
Iterative methods which have high convergence order are crucial in computational mathematics since the iterates produce sequences converging to the root of a non-linear equation. A plethora of applications in chemistry and physics require the solution of non-linear equations in abstract spaces iteratively. The derivation of the order of the iterative methods requires expansions using Taylor series formula and higher-order derivatives not present in the method. Thus, these results cannot prove the convergence of the iterative method in these cases when such higher-order derivatives are non-existent. However, these methods may still converge. Our motivation originates from the need to handle these problems. No error estimates are given that are controlled by constants. The process introduced in this paper discusses both the local and the semi-local convergence analysis of two step fifth and multi-step 5+3r order iterative methods obtained using only information from the operators on these methods. Finally, the novelty of our process relates to the fact that the convergence conditions depend only on the functions and operators which are present in the methods. Thus, the applicability is extended to these methods. Numerical applications complement the theory. Full article
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