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Journal of Scientific Computing

, Volume 78, Issue 3, pp 1659–1659 | Cite as

Correction to: A Fourth-Order Kernel-Free Boundary Integral Method for the Modified Helmholtz Equation

  • Yaning Xie
  • Wenjun YingEmail author
Correction
  • 135 Downloads

1 Correction to: Journal of Scientific Computing  https://doi.org/10.1007/s10915-018-0821-8

The original version of this article contained mistakes in equations. The corrected equations are given below:

In Eqs. 4447485152 and 53, the minus sign before the Kappa should be changed to “plus” sign.
$$\begin{aligned} \left\{ \begin{array}{l} (x')^2 [u_{xx}] + 2 x' y' [u_{xy}] + (y')^2 [u_{yy}] = \varphi _{ss} - \big \{ x''(s) [u_x] + y''(s) [u_y] \big \} \\ x' y' [u_{xx}] + \big \{ (y')^2 - (x')^2 \big \} [u_{xy}] - x'y' [u_{yy}] = \psi _s - y'' [u_x] + x'' [u_y] \\ {[} u_{xx} ] + [ u_{yy} ] = f +\kappa [u] \end{array} \right. . \end{aligned}$$
(44)
$$\begin{aligned} {[}u_{xxx}] + [u_{xyy}]= & {} f_x+\kappa \, [u_x],\end{aligned}$$
(47)
$$\begin{aligned} {[}u_{xxy}] + [u_{yyy}]= & {} f_y+\kappa \, [u_y]. \end{aligned}$$
(48)
$$\begin{aligned}{}[u_{xxxx}] + [u_{xxyy}]= & {} f_{xx}+\kappa [u_{xx}], \end{aligned}$$
(51)
$$\begin{aligned}{}[u_{xxxy}] + [u_{xyyy}]= & {} f_{xy}+\kappa [u_{xy}], \end{aligned}$$
(52)
$$\begin{aligned}{}[u_{xxyy}] + [u_{yyyy}]= & {} f_{yy}+\kappa [u_{yy}], \end{aligned}$$
(53)
The original article has been corrected.

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Mathematical SciencesShanghai Jiao Tong UniversityMinhang, ShanghaiPeople’s Republic of China
  2. 2.School of Mathematical Sciences, MOE-LSC and Institute of Natural SciencesShanghai Jiao Tong UniversityMinhang, ShanghaiPeople’s Republic of China

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