Direct solution of ill‐posed boundary value problems by radial basis function collocation method
Direct solution of ill‐posed boundary value problems by radial basis function collocation method
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DOI：
10.1002/nme.1362
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发表时间：
2005-09
影响因子：
2.9
通讯作者：
A. Cheng;J. Cabral
中科院分区：
文献类型：
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作者：
A. Cheng;J. Cabral
不适定边值问题的数值解通常需要迭代过程。在一个典型的解决方案中，不适定问题首先通过假设缺失的边界值转换为适定问题。新的问题是解决了一个传统的数值技术和解决方案是检查对未使用的数据。使用优化方案迭代地解决该问题，直到实现收敛。本文件提供了一种不同的程序。使用径向基函数配点法，我们证明了某些不适定问题的解决方案可以在没有迭代的情况下完成。该方法不仅计算效率高、精度高，而且避免了迭代法可能存在的稳定性问题。版权所有© 2005年约翰威利父子有限公司。
Numerical solution of ill‐posed boundary value problems normally requires iterative procedures. In a typical solution, the ill‐posed problem is first converted to a well‐posed one by assuming the missing boundary values. The new problem is solved by a conventional numerical technique and the solution is checked against the unused data. The problem is solved iteratively using optimization schemes until convergence is achieved. The present paper offers a different procedure. Using the radial basis function collocation method, we demonstrate that the solution of certain ill‐posed problems can be accomplished without iteration. This method not only is efficient and accurate, but also circumvents the stability problem that can exist in the iterative method. Copyright © 2005 John Wiley & Sons, Ltd.