Article ID Journal Published Year Pages File Type
4638508 Journal of Computational and Applied Mathematics 2015 14 Pages PDF
Abstract

Orthogonal polynomials on the product domain [a1,b1]×[a2,b2][a1,b1]×[a2,b2] with respect to the inner product 〈f,g〉S=∫a1b1∫a2b2∇f(x,y)⋅∇g(x,y)w1(x)w2(y)dxdy+λf(c1,c2)g(c1,c2) are constructed, where wiwi is a weight function on [ai,bi][ai,bi] for i=1,2i=1,2, λ>0λ>0, and (c1,c2)(c1,c2) is a fixed point. The main result shows how an orthogonal basis for such an inner product can be constructed for certain weight functions, in particular, for product Laguerre and product Gegenbauer weight functions, which serve as primary examples.

Related Topics
Physical Sciences and Engineering Mathematics Applied Mathematics
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