论文信息 - Euler-Maclaurin expansions for integrals over triangles and squares of functions having algebraic/logarithmic singularities along an edge

Euler-Maclaurin expansions for integrals over triangles and squares of functions having algebraic/logarithmic singularities along an edge

Abstract We derive and analyze the properties of Euler-Maclaurin expansions for the differences ∝ s ∝ x s ( log x) s′ f(x, y) − Q h s ¦f|, s > ·· 1, s′ = 0,1 , where S denotes either the simplex {(x, y)¦x + y ⩽ 1, x ⩾ 0, y ⩾ 0} or the square {(x, y)¦0 ⩽ x ⩽ 1, 0 ⩽ y ⩽ 1}, and Q h s ¦f¦ is a combination of one-dimensional generalized trapezoidal rule approximations.

Avram Sidi | A. Sidi

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