arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 2001.00616math.APcs.NAmath.NA
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用全局参数延拓全局解曲线

Continuation of global solution curves using global parameters

Philip Korman, Dieter S. Schmidt

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32 pages, 15 figures
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摘要：

本文通过对整体参数的延拓，给出了整体解曲线的理论结果和数值计算。当全局参数变化时，解曲线上的每个点都被直接计算，因此解曲线的所有转弯以及它的不同分支都自动出现在计算机屏幕上。对于径向$p$ -Laplace方程，我们给出了P. Korman [15]正则化变换的简化推导，并使用该变换进行更精确的数值计算。虽然对于$p>2$的解决方案是不属于类$C^2$，我们表明，他们的形式$w(r^{\frac{p}{2(p-1)}})$，其中$w(z)$是类$C^2$。分叉图也计算非自治问题，并为四阶方程模拟弹性梁。我们表明，第一谐波的解决方案也可以作为一个整体参数。

英文摘要：

This paper provides both the theoretical results and numerical calculations of global solution curves, by continuation in global parameters. Each point on the solution curves is computed directly as the global parameter is varied, so that all of the turns that the solution curves make, as well as its different branches, appear automatically on the computer screen. For radial $p$-Laplace equations we present a simplified derivation of the regularizing transformation from P. Korman [15], and use this transformation for more accurate numerical computations. While for $p>2$ the solutions are not of class $C^2$, we show that they are of the form $w(r^{\frac{p}{2(p-1)}})$, where $w(z)$ is of class $C^2$. Bifurcation diagrams are also calculated for non-autonomous problems, and for the fourth order equations modeling elastic beams. We show that the first harmonic of the solution can also serve as a global parameter.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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