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首页> 外文会议>International Conference on Computational Science - ICCA 2003 Pt.2 Jun 2-4, 2003 Melbourne, Australia and St. Petersburg, Russia >To Numerical Solution of Singular Perturbed Equations Transformed to the Best Argument
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To Numerical Solution of Singular Perturbed Equations Transformed to the Best Argument

机译：奇异摄动方程最佳解的数值解

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摘要

We consider the numerical solution of initial value problem for the system of ordinary differential singular perturbed equations. The integral curve of the problem is constructed using method of continuation with respect to a parameter. We can choose the best parameter in any step of integration process. It is found that the best argument of the Cauchy problem is the arc length of the integral curve of the problem. Transformed to the best argument Cauchy problem has a number advantages in comparison with the Cauchy problem over the usual statement. The right - hand side of each transformed equation does not exceed unit. Moreover, the squared norm of the system right - hand sides is always equal to unit. Also the suggested transformation reduces the difficulties that are typical for stiff systems. The efficiency of the approach is shown on test examples.
机译：我们考虑了常微分奇异摄动方程组初值问题的数值解。使用关于参数的连续方法构造问题的积分曲线。我们可以在集成过程的任何步骤中选择最佳参数。发现柯西问题的最佳论据是问题积分曲线的弧长。与柯西问题相比，与通常的陈述相比，转换为最佳论证的柯西问题具有许多优势。每个变换方程的右手边不超过单位。此外，系统右侧的平方范数始终等于单位。同样，建议的转换减少了刚性系统通常遇到的困难。测试示例显示了该方法的效率。

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