full
search.png

Search

close.png

Cancel

arrow
Volume 5, Issue 5
The Recursive Formulation of Particular Solutions for Some Elliptic PDEs with Polynomial Source Functions

J. Ding, H. Y. Tian & C. S. Chen

Commun. Comput. Phys., 5 (2009), pp. 942-958.

Published online: 2009-05

Preview Full PDF 3027 28998

Cited by

google scholar semantic scholar
Export citation
  • Abstract

In this paper we develop an efficient meshless method for solving inhomogeneous elliptic partial differential equations. We first approximate the source function by Chebyshev polynomials. We then focus on how to find a polynomial particular solution when the source function is a polynomial. Through the principle of the method of undetermined coefficients and a proper arrangement of the terms for the polynomial particular solution to be determined, the coefficients of the particular solution satisfy a triangular system of linear algebraic equations. Explicit recursive formulas for the coefficients of the particular solutions are derived for different types of elliptic PDEs. The method is further incorporated into the method of fundamental solutions for solving inhomogeneous elliptic PDEs. Numerical results show that our approach is efficient and accurate.

  • Keywords

  • AMS Subject Headings

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address
  • BibTex
  • RIS
  • TXT
@Article{CiCP-5-942, author = {J. Ding, H. Y. Tian and C. S. Chen}, title = {The Recursive Formulation of Particular Solutions for Some Elliptic PDEs with Polynomial Source Functions}, journal = {Communications in Computational Physics}, year = {2009}, volume = {5}, number = {5}, pages = {942--958}, abstract = {

In this paper we develop an efficient meshless method for solving inhomogeneous elliptic partial differential equations. We first approximate the source function by Chebyshev polynomials. We then focus on how to find a polynomial particular solution when the source function is a polynomial. Through the principle of the method of undetermined coefficients and a proper arrangement of the terms for the polynomial particular solution to be determined, the coefficients of the particular solution satisfy a triangular system of linear algebraic equations. Explicit recursive formulas for the coefficients of the particular solutions are derived for different types of elliptic PDEs. The method is further incorporated into the method of fundamental solutions for solving inhomogeneous elliptic PDEs. Numerical results show that our approach is efficient and accurate.

}, issn = {1991-7120}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/cicp/7772.html} }
TY - JOUR T1 - The Recursive Formulation of Particular Solutions for Some Elliptic PDEs with Polynomial Source Functions AU - J. Ding, H. Y. Tian & C. S. Chen JO - Communications in Computational Physics VL - 5 SP - 942 EP - 958 PY - 2009 DA - 2009/05 SN - 5 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/cicp/7772.html KW - AB -

In this paper we develop an efficient meshless method for solving inhomogeneous elliptic partial differential equations. We first approximate the source function by Chebyshev polynomials. We then focus on how to find a polynomial particular solution when the source function is a polynomial. Through the principle of the method of undetermined coefficients and a proper arrangement of the terms for the polynomial particular solution to be determined, the coefficients of the particular solution satisfy a triangular system of linear algebraic equations. Explicit recursive formulas for the coefficients of the particular solutions are derived for different types of elliptic PDEs. The method is further incorporated into the method of fundamental solutions for solving inhomogeneous elliptic PDEs. Numerical results show that our approach is efficient and accurate.

J. Ding, H. Y. Tian and C. S. Chen. (2009). The Recursive Formulation of Particular Solutions for Some Elliptic PDEs with Polynomial Source Functions. Communications in Computational Physics. 5 (5). 942-958. doi:
Copy to clipboard
BibteX RIS TXT
The citation has been copied to your clipboard