Applied Mathematics and Mechanics

, Volume 14, Issue 3, pp 201–207 | Cite as

A high convergent precision exact analytic method for differential equation with variable coefficients

  • Ji Zhen-yi
  • Yeh Kai-yuan


The exact analytic method was given by [1]. It can be used for arbitrary variable coefficient differential equations and the solution obtained can have the second order convergent precision. In this paper, a new high precision algorithm is given based on [1], through a bending problem of variable cross-section beams. It can have the fourth convergent precision without increasing computation work. The present computation method is not only simple but also fast. The numerical examples are given at the end of this paper which indicate that the high convergent precision can be obtained using only a few elements. The correctness of the theory in this paper is confirmed.

Key words

exact analytic method bending of beam high convergent precision 


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  1. [1]
    Ji Zhen-yi and Yeh Kai-yuan, Exact analytic method for solving arbitrary variable coefficient differential equation,Applied Mathematics and Mechanics,10, 10 (1989), 841–852.MathSciNetCrossRefGoogle Scholar
  2. [2]
    Yeh Kai-yuan and Ji Zhen-yi, An exact analytic method applied to nonhomogeneous ring-and string-stiffened cylindrical shell,Applied Mathematics and Mechanics,10, 9 (1989), 785–796.CrossRefGoogle Scholar
  3. [3]
    Ji Zhen-yi and Yeh Kai-yuan, General solution on nonlinear buckling of nonhomogeneous axial symmetric ring-and stringer-stiffened cylindrical shell,Computer & Structure,34,4 (1990), 585–591.CrossRefGoogle Scholar

Copyright information

© Shanghai University of Technology (SUT) 1993

Authors and Affiliations

  • Ji Zhen-yi
    • 1
  • Yeh Kai-yuan
    • 2
  1. 1.Anhui Architectural Industry CollegeHefei
  2. 2.Lanzhou UniversityLanzhou

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