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Eigenfunctions and the Dirichlet problem for the Classical Kimura Diffusion Operator

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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
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  Data: Eigenfunctions and the Dirichlet problem for the Classical Kimura Diffusion Operator
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  Data: <searchLink fieldCode="AR" term="%22Epstein%2C+Charles+L%2E%22">Epstein, Charles L.</searchLink><br /><searchLink fieldCode="AR" term="%22Wilkening%2C+Jon%22">Wilkening, Jon</searchLink>
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  Data: Mathematics<br />Quantitative Biology
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  Data: 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.<br />Comment: To appear in SIAM Journal of Applied Math
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      – SubjectFull: Mathematics - Analysis of PDEs
        Type: general
      – SubjectFull: Mathematics - Numerical Analysis
        Type: general
      – SubjectFull: Quantitative Biology - Populations and Evolution
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      – TitleFull: Eigenfunctions and the Dirichlet problem for the Classical Kimura Diffusion Operator
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              Y: 2015
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