Abstract
The boundary knot method (BKM) is a boundary meshless method for solving homogeneous boundary value problems. The fact that the BKM uses non-singular general solution without the need of source points outside the domain is at the expense of the accuracy when compared to the well-known method of fundamental solutions. In this paper, a new approach called the enhanced BKM (EBKM) is proposed to greatly improve the accuracy of the BKM by introducing fictitious sources which can be placed inside and/or outside the domain quite freely. We also adopt various techniques to place these fictitious sources in an optimal way.
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Disclosure statement
No potential conflict of interest was reported by the author(s).
Appendix
We provide the following MATLAB code for the solution of Example 1 using LOOCV. For the case using effective condition number, Lines 45–47 can be replaced by Lines 48–51. The following code can be run using MATLAB version R2021a or above.