Applied Mathematics and Mechanics (English Edition) ›› 2002, Vol. 23 ›› Issue (3): 241-248.

• 论文 •    下一篇

LINEARIZATION AND CORRECTION METHOD FOR NONLINEAR PROBLEMS

何吉欢   

  1. Shanghai University; Shanghai Institute of Applied Mathematics and Mechanics, Shanghai 200072, P. R. China
  • 收稿日期:2001-01-08 修回日期:2001-08-28 出版日期:2002-03-18 发布日期:2002-03-18

LINEARIZATION AND CORRECTION METHOD FOR NONLINEAR PROBLEMS

HE Ji-huan   

  1. Shanghai University; Shanghai Institute of Applied Mathematics and Mechanics, Shanghai 200072, P. R. China
  • Received:2001-01-08 Revised:2001-08-28 Online:2002-03-18 Published:2002-03-18

摘要: A new perturbation-like technique called linearization and correction method is proposed. Contrary to the traditional perturbation techniques, the present theory does not assume that the solution is expressed in the form of a power series of small parameter. To obtain an asymptotic solution of nonlinear system, the technique first searched for a solution for the linearized system, then a correction was added to the linearized solution. So the obtained results are uniformly valid for both weakly and strongly nonlinear equations.

Abstract: A new perturbation-like technique called linearization and correction method is proposed. Contrary to the traditional perturbation techniques, the present theory does not assume that the solution is expressed in the form of a power series of small parameter. To obtain an asymptotic solution of nonlinear system, the technique first searched for a solution for the linearized system, then a correction was added to the linearized solution. So the obtained results are uniformly valid for both weakly and strongly nonlinear equations.

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