A numerical method to approximate the solutions of nonlinear systems in densifiable sets

被引：0
|
作者：
Garcia, G. [1 ]
机构：
[1] Univ Nacl Educ Distancia UNED, Dept Matemat, CL Candalix S-N, Elche 03202, Alicante, Spain
来源：
NUMERICAL ALGORITHMS | 2024年 / 96卷 / 04期
关键词：
Nonlinear equations; Numerical methods; Densifiable sets; alpha-dense curves; CONTINUOUS GLOBAL OPTIMIZATION; EQUATIONS; GENERATION;
D O I：
10.1007/s11075-023-01690-y
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In the present paper, we study the approximation of solutions (if any) of a system of equations, where the only condition required to the involved functions is to be continuous. To be more precise, by using the so called alpha-dense curves, if the given system has some solution in a densifiable set we propose a method, which only use evaluations of single variable functions, to approximate at least one solution of the system in such set. The feasibility and reliability of the proposed method is illustrated by several examples, and its drawbacks are also discussed.
引用
收藏
页码：1925 / 1943
页数：19
相关论文
共 50 条
  • [1] A new method for approximate analytical solutions to nonlinear oscillations of nonnatural systems
    Wu, BS
    Lim, CW
    He, LH
    NONLINEAR DYNAMICS, 2003, 32 (01) : 1 - 13
  • [2] A New Method for Approximate Analytical Solutions to Nonlinear Oscillations of Nonnatural Systems
    B. S. Wu
    C. W. Lim
    L. H. He
    Nonlinear Dynamics, 2003, 32 : 1 - 13
  • [3] Numerical integration method to determine periodic solutions of nonlinear systems
    Torii, Takao
    Morita, Nobuyoshi
    Yasuda, Kimihiko
    Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, Vol 1, Pts A-C, 2005, : 1625 - 1630
  • [4] An approximate method for finding periodic solutions to systems of nonlinear ordinary differential equations
    Perov, AI
    DOKLADY MATHEMATICS, 2003, 68 (02) : 158 - 162
  • [5] Approximate Solutions for the Nonlinear Systems of Algebraic Equations Using the Power Series Method
    Khader, M. M.
    Adel, M.
    APPLICATIONS AND APPLIED MATHEMATICS-AN INTERNATIONAL JOURNAL, 2020, 15 (02): : 1267 - 1274
  • [6] Enhanced Multistage Homotopy Perturbation Method: Approximate Solutions of Nonlinear Dynamic Systems
    Olvera, Daniel
    Elias-Zuniga, Alex
    ABSTRACT AND APPLIED ANALYSIS, 2014,
  • [7] APPROXIMATE DETERMINATION OF PERIODIC SOLUTIONS IN NONLINEAR SYSTEMS
    CHANDRA, J
    FLEISHMA.BA
    SIAM REVIEW, 1966, 8 (04) : 560 - &
  • [8] Finding sets of solutions to systems of nonlinear inequalities
    Evtushenko, Yu. G.
    Posypkin, M. A.
    Rybak, L. A.
    Turkin, A. V.
    COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS, 2017, 57 (08) : 1241 - 1247
  • [9] Finding sets of solutions to systems of nonlinear inequalities
    Yu. G. Evtushenko
    M. A. Posypkin
    L. A. Rybak
    A. V. Turkin
    Computational Mathematics and Mathematical Physics, 2017, 57 : 1241 - 1247
  • [10] A method to find approximate solutions of first-order systems of nonlinear ordinary equations
    Alvarez-Sanchez, J. J.
    Gadella, M.
    Lara, L. P.
    MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2021, 44 (13) : 10014 - 10031
12345