A multiple-scale Pascal polynomial triangle solving elliptic equations and inverse Cauchy problems

作者：Liu Chein Shan; Kuo Chung Lun^*

来源：Engineering Analysis with Boundary Elements, 2016, 62: 35-43.

DOI：10.1016/j.enganabound.2015.09.003

• Multi-scale polynomial expansion
• Pascal triangle
• Elliptic PDEs
• Inverse Cauchy problems

The polynomial expansion method is a useful tool to solve partial differential equations (PDEs). However, the researchers seldom use it as a major medium to solve PDEs due to its highly ill-conditioned behavior. We propose a single-scale and a multiple-scale Pascal triangle formulations to solve the linear elliptic PDEs in a simply connected domain equipped with complex boundary shape. For the former method a constant parameter R-0 is required, while in the latter one all introduced scales are automatically determined by the collocation points. Then we use the multiple-scale method to solve the inverse Cauchy problems, which is very accurate and very stable against large noise to 20%. Numerical results confirm the validity of the present multiple-scale Pascal polynomial expansion method.

• 出版日期2016-1