强非线性振动方程渐近解的数值验证及其误差分析

Numeircal Verification and Error Analysis Ofasymtotic Solutions of Strongly Nonlinear Oscillation

Kuzmak-Luke多尺度法能有效地用于求解某些带慢变参数的强非线性振动.一种数值阶验证技术用于验证该渐近解对小参数是一致有效的.算例的误差分析说明用Kuzmak-Luke多尺度法求得的渐近解是一致有效的,且其误差在数值上近似为小参数ε的十分之一.

The multiple scales method of Kuzmak-Luke can be efficiently applied to obtain the solutions of strongly nonlinear oscillators with slowly varying parameters. A technique of numerical order verification is applied to verify that the asymptotic solutions are uniformly valid for small parameter. A numerical comparison of error shows that the asymptotic solutions obtained by the multiple scales method of Kuzmak-Luke are uniformly valid, and the errors are about one-tenth of the small parameter ε.