Solving the First Order Differential Equations using Newton's Interpolation and Lagrange Polynomial

被引：0
|
作者：
Neamvonk, Apichat [1 ]
Sriponpaew, Boonyong [1 ]
机构：
[1] Burapha Univ, Fac Sci, Dept Math, Chon Buri, Thailand
来源：
EUROPEAN JOURNAL OF PURE AND APPLIED MATHEMATICS | 2023年 / 16卷 / 02期
关键词：
Numerical method; Initial value problems; Newton's interpolation; Lagrange polynomial;
D O I：
10.29020/nybg.ejpam.v16i2.4727
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we use both Newton's interpolation and Lagrange polynomial to create cubic polynomials for solving the initial value problems. By this new method, it is simple to solve linear and nonlinear first order ordinary differential equations and to yield and implement actual precise results. Some numerical examples are provided to test the performance and illustrate the efficiency of the method.
引用
收藏
页码：965 / 974
页数：10
相关论文
共 50 条
  • [1] Solving second order ordinary differential equations by using Newton's interpolation and Aitken's methods
    Mbagwu, J. P. C.
    Tunc, Cemil
    Enyoh, C. E.
    Onwuemekaa, J. I.
    INTERNATIONAL JOURNAL OF NONLINEAR ANALYSIS AND APPLICATIONS, 2022, 13 (01): : 1057 - 1066
  • [2] POLYNOMIAL INTERPOLATION - LAGRANGE VERSUS NEWTON
    WERNER, W
    MATHEMATICS OF COMPUTATION, 1984, 43 (167) : 205 - 217
  • [3] Solving one Class of Systems of the Polynomial Volterra Equations of the First Kind by Newton's Method
    Solodusha, Svetlana
    2017 CONSTRUCTIVE NONSMOOTH ANALYSIS AND RELATED TOPICS (DEDICATED TO THE MEMORY OF V.F. DEMYANOV) (CNSA), 2017, : 299 - 303
  • [4] Barycentric Lagrange interpolation method for solving Love's integral equations
    Shoukralla, E. S.
    Ahmed, B. M.
    BOUNDARY VALUE PROBLEMS, 2023, 2023 (01)
  • [5] Barycentric Lagrange interpolation method for solving Love’s integral equations
    E. S. Shoukralla
    B. M. Ahmed
    Boundary Value Problems, 2023
  • [6] Lagrange-Noether method for solving second-order differential equations
    Wu Hui-Bin
    Wu Run-Heng
    CHINESE PHYSICS B, 2009, 18 (09) : 3647 - 3650
  • [7] Lagrange-Noether method for solving second-order differential equations
    吴惠彬
    吴润衡
    Chinese Physics B, 2009, 18 (09) : 3647 - 3650
  • [8] On the numerical stability of Newton's formula for Lagrange interpolation
    de Camargo, Andre Pierro
    JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2020, 365
  • [9] Solving Nonlinear Wave Equations Based on Barycentric Lagrange Interpolation
    Yuan, Hongwang
    Wang, Xiyin
    Li, Jin
    JOURNAL OF NONLINEAR MATHEMATICAL PHYSICS, 2024, 31 (01)
  • [10] Lagrange interpolation polynomials for solving nonlinear stochastic integral equations
    Ikram Boukhelkhal
    Rebiha Zeghdane
    Numerical Algorithms, 2024, 96 : 583 - 618
12345