Volume 12, Issue 4
Solving Fourth-Order PDEs using the LMAPS

Cheng Deng, Hui Zheng, Yan Shi & C. S. Chen

Adv. Appl. Math. Mech., 12 (2020), pp. 920-939.

Published online: 2020-06

Preview Purchase PDF 11 776
Export citation
  • Abstract

To overcome the difficulty for solving fourth order partial differential equations (PDEs) using localized methods, we introduce and extend a recent method to decompose the particular solution of such equation into particular solutions of two second-order differential equations using radial basis functions (RBFs). In this way, the localized method of approximate particular solutions (LMAPS) can be used to directly solve a fourth-order PDE without splitting it into two second-order problems. The closed-form particular solutions for polyharmonic splines RBFs augmented with polynomial basis functions for Helmholtz-type equations are the cores of the solution process. Several novel techniques are proposed to further improve the accuracy and efficiency. Four numerical examples are presented to show the effectiveness of our approach.

  • Keywords

Localized method of approximate particular solutions, Helmholtz-type operator, fourth-order partial differential equation, polynomial basis functions, polyharmonic splines of RBFs.

  • AMS Subject Headings

65Y04, 35K05

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

zhenghui@ncu.edu.cn ( Hui Zheng)

  • BibTex
  • RIS
  • TXT
Copy to clipboard
The citation has been copied to your clipboard