Applied Mathematics and Mechanics (English Edition) ›› 1995, Vol. 16 ›› Issue (5): 429-435.

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COMPUTER ALGEBRA-PERTURBATION SOLUTION TO A NONLINEAR WAVE EQUATION

Wang Ming-qi, Dai Shi-qiang   

  1. Shanghai Univkrsity; Shanghai Institute of Applied Mathematics and Mechanics, Shanghai 200072, P. R. China
  • Received:1994-07-22 Online:1995-05-18 Published:1995-05-18
  • Supported by:

    Project supported by the National Natural Science Foundation of China and Shanghai Municiple Natural Science Foundation

Abstract: In this paper, the higher-order asymptotic solution to the Cauchy problem of a nonlinear wave equation is found by using a computer algebra-perturbation method. The secular terms in the solution from straightforward expansions, are eliminated with the straining of characteristic coordinates and the use of the renormalization technique, and the four-term uniformly valid solution is obtained with the symbolic computation by using a computer algebra system. The comparison of the derived asymptotic solution dnd the numerical solution shows that they coincide with each other for smaller ε and agree quite well for larger ε(e. g., e=0.25)

Key words: nonlinear wave, perturbation, computer algebra, renormalization technique, approximate analytical method of characteristics, anisotropy, viscoelasticity, wave equation, eigen theory

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