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Numerical Method for a Cauchy Problem for Multi-Dimensional Laplace Equation with Bilateral Exponential Kernel

Author

Listed:
  • Xianli Lv

    (School of Mathematics and Statistics, Ningxia University, Yinchuan 750021, China)

  • Xiufang Feng

    (School of Mathematics and Statistics, Ningxia University, Yinchuan 750021, China)

Abstract

This study examined a Cauchy problem for a multi-dimensional Laplace equation with mixed boundary. This problem is severely ill-posed in the sense of Hadamard. To solve this problem, a mollification approach is suggested based on a bilateral exponential kernel and this is a new approach. The stable error estimates are obtained under the priori and posteriori rule, in which the numerical findings are much influenced by the unknown a priori information. An error estimate between the exact and regular solution is given. A numerical experiment of interest reveals that our procedure is efficient and stable for perturbation noise in the data.

Suggested Citation

  • Xianli Lv & Xiufang Feng, 2023. "Numerical Method for a Cauchy Problem for Multi-Dimensional Laplace Equation with Bilateral Exponential Kernel," Mathematics, MDPI, vol. 11(8), pages 1-20, April.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:8:p:1855-:d:1123073
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