Transformation of an axialsymmetric disk problem for the helmholtz equation into an ordinary differential equation

Gorenflo, Norbert

doi:10.1007/bf01196517

Search citation statements

Order By: Relevance

Paper Sections

Select...

Introduction1

Citation Types

Supporting

Mentioning

Contrasting

Year Published

1999

2012

Publication Types

Select...

Article5

Relationship

Self Cite1

Independent4

Authors

Journals

Cited by 5 publications

(1 citation statement)

References 8 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…53 (2002) A new explicit solution method for the diffraction through a slit 879 of y is a generalization of a differential equation for spheroidal wave functions ([5, Corollary 3.1]). (In [8] an analogous system of ordinary differential equations has been derived for the boundary integral equation arising from the axialsymmetric disk problem for the Helmholtz equation. )…”

Section: Introductionmentioning

confidence: 99%

Untitled

Gorenflo

2002

Z angew Math Phys

View full text Add to dashboard Cite

The two-dimensional time harmonic problem of diffraction through a slit is considered for arbitrary Dirichlet data, prescribed in the slit; on the screen itself the wavefield satisfies a homogeneous Neumann boundary condition. First of all, a sequence of special Dirichlet data is constructed, for each of these data the resulting wavefield can be expressed in closed form. The sequence can be constructed in a way which yields an orthonormal basis of Dirichlet data. After this has been done, arbitrary Dirichlet data can be expanded into a series of the orthonormal basis functions; this results in a representation for the searched wavefield. The presented method gives a deep insight into the mathematical structure of the problem.

show abstract

Section: Introductionmentioning

confidence: 99%