Eigenfunctions and the Dirichlet problem for the Classical Kimura Diffusion Operator
| Title: | Eigenfunctions and the Dirichlet problem for the Classical Kimura Diffusion Operator |
|---|---|
| Authors: | Epstein, Charles L., Wilkening, Jon |
| Publication Year: | 2015 |
| Collection: | Mathematics Quantitative Biology |
| Subject Terms: | Mathematics - Analysis of PDEs, Mathematics - Numerical Analysis, Quantitative Biology - Populations and Evolution |
| More Details: | We study the classical Kimura diffusion operator defined on the n-simplex, $$L^{Kim}=\sum_{1\leq i,j\leq n+1}x_ix_j\partial_{x_i}\partial_{x_j}$$ We give novel constructions for the basis of eigenpolynomials, and the solution to the inhomogeneous Dirichlet problem, which are well adapted to numerical applications. Our solution of the Dirichlet problem is quite explicit and provides a precise description of the singularities that arise along the boundary. Comment: To appear in SIAM Journal of Applied Math |
| Document Type: | Working Paper |
| Access URL: | http://arxiv.org/abs/1508.01482 |
| Accession Number: | edsarx.1508.01482 |
| Database: | arXiv |
| Description not available. |