Computer Algebra-Perturbation Solution to a Nonlinear Wave Equation

Wang Ming-qi; Dai Shi-qiang

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Article Navigation > Applied Mathematics and Mechanics > 1995 > 16(5): 403-408

Wang Ming-qi, Dai Shi-qiang. Computer Algebra-Perturbation Solution to a Nonlinear Wave Equation[J]. Applied Mathematics and Mechanics, 1995, 16(5): 403-408.

Citation:

Wang Ming-qi, Dai Shi-qiang. Computer Algebra-Perturbation Solution to a Nonlinear Wave Equation[J]. Applied Mathematics and Mechanics, 1995, 16(5): 403-408.

Citation:

Wang Ming-qi, Dai Shi-qiang. Computer Algebra-Perturbation Solution to a Nonlinear Wave Equation[J]. Applied Mathematics and Mechanics, 1995, 16(5): 403-408.

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Computer Algebra-Perturbation Solution to a Nonlinear Wave Equation

Shanghai University, Shanghai Institute of Applied Mathematics and Mechanics, Shanghai 200072, P. R. China

Received Date: 1994-07-22
Publish Date: 1995-05-15

Abstract

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).
- nonlinear wave,
- perturbation,
- computer algebra,
- renormalization technique,
- approximate analytical method of characteristics

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References(11)

References

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