The Solutions of Legendre's and Chebyshev's Differential Equations by Using the Differential Transform Method

被引：1
|
作者：
Alotaibi, A. M. [1 ]
El-Moneam, M. A. [2 ]
Badr, Badr S. [3 ]
机构：
[1] Univ Tabuk, Fac Sci, Dept Math, POB 741, Tabuk 71491, Saudi Arabia
[2] Jazan Univ, Fac Sci, Math Dept, Jazan, Saudi Arabia
[3] Tanta Univ, Fac Sci, Math Dept, Tanta, Egypt
来源：
MATHEMATICAL PROBLEMS IN ENGINEERING | 2022年 / 2022卷
关键词：
BOUNDARY-VALUE-PROBLEMS;
D O I：
10.1155/2022/8893695
中图分类号：
T [工业技术];
学科分类号：
08 ;
摘要：
Chebyshev's and Legendre's differential equations' solutions are solved employing the differential transform method (DTM) and the power series method (PSM) in this study. This research shows that this method is efficient and effective in discovering Chebyshev's and Legendre's differential equation (DE) series solutions and that it can reduce calculation size when compared to other methods.
引用
收藏
页数：9
相关论文
共 50 条
  • [1] An Extended Legendre Wavelet Method for Solving Differential Equations with Non-Analytic Solutions
    Mohammadi, F.
    JOURNAL OF MATHEMATICAL EXTENSION, 2014, 8 (04) : 55 - 74
  • [2] Numerical Solutions of Fractional Variable Order Differential Equations via Using Shifted Legendre Polynomials
    Shah, Kamal
    Naz, Hafsa
    Abdeljawad, Thabet
    Khan, Aziz
    Alqudah, Manar A.
    CMES-COMPUTER MODELING IN ENGINEERING & SCIENCES, 2023, 134 (02): : 941 - 955
  • [3] Solution of conformable fractional ordinary differential equations via differential transform method
    Unal, Emrah
    Gokdogan, Ahmet
    OPTIK, 2017, 128 : 264 - 273
  • [4] A LEGENDRE WAVELET COLLOCATION METHOD FOR SOLVING NEUTRAL DELAY DIFFERENTIAL EQUATIONS
    Ahmed, Uzair
    Faheem, Mo
    Khan, Arshad
    Manchanda, Geetan
    MISKOLC MATHEMATICAL NOTES, 2024, 25 (01) : 35 - 48
  • [5] RIGOROUS NUMERICS FOR NONLINEAR DIFFERENTIAL EQUATIONS USING CHEBYSHEV SERIES
    Lessard, Jean-Philippe
    Reinhardt, Christian
    SIAM JOURNAL ON NUMERICAL ANALYSIS, 2014, 52 (01) : 1 - 22
  • [6] Fifth-kind orthonormal Chebyshev polynomial solutions for fractional differential equations
    Abd-Elhameed, W. M.
    Youssri, Y. H.
    COMPUTATIONAL & APPLIED MATHEMATICS, 2018, 37 (03) : 2897 - 2921
  • [7] On Solutions of Matrix Initial Value Problems by Using Differential Transform Method and Convolution
    Altun, Omer
    Kilicman, Adem
    INTERNATIONAL CONFERENCE ON MATHEMATICAL SCIENCES AND STATISTICS 2013 (ICMSS2013), 2013, 1557 : 191 - 194
  • [8] Numerical solution of fractional differential equations using fractional Chebyshev polynomials
    Ozturk, Yalcin
    Unal, Mutlu
    ASIAN-EUROPEAN JOURNAL OF MATHEMATICS, 2022, 15 (03)
  • [9] MONOTONE ITERATIVE METHOD FOR SOLUTIONS OF FRACTIONAL DIFFERENTIAL EQUATIONS
    Padhi, Seshadev
    Prasad, B. S. R., V
    Srivastava, Satyam Narayan
    Bhuyan, Shasanka Dev
    MEMOIRS ON DIFFERENTIAL EQUATIONS AND MATHEMATICAL PHYSICS, 2019, 77 : 59 - 69
  • [10] METHOD OF UPPER AND LOWER SOLUTIONS FOR FRACTIONAL DIFFERENTIAL EQUATIONS
    Lin, Legang
    Liu, Xiping
    Fang, Haiqin
    ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2012,
12345