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Recurrence relations for spherical waves
Author(s) -
James Geoffrey C.
Publication year - 1996
Publication title -
radio science
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.371
H-Index - 84
eISSN - 1944-799X
pISSN - 0048-6604
DOI - 10.1029/96rs02790
Subject(s) - scalar (mathematics) , cartesian coordinate system , algebraic number , spherical wave , mathematics , recurrence relation , spherical coordinate system , gravitational wave , symbolic computation , mathematical analysis , physics , classical mechanics , geometry , optics , quantum mechanics
This paper derives new recurrence relations for scalar spherical waves in Cartesian coordinates and compares the performance of these relations with that of traditional recurrence relations. They are numerically stable for travelling waves and some standing waves, and are faster for evaluating scalar spherical waves up to order 40 on a nonspherical surface. Because of their algebraic simplicity, they will be especially useful for symbolic‐algebra computer programs, allowing explicit expressions for scalar and vector spherical waves to be obtained using a succinct procedure.