ISSN:
1420-9039
Quelle:
Springer Online Journal Archives 1860-2000
Thema:
Mathematik
,
Physik
Notizen:
Abstract Based on the fact that the complete set of eigenfunctions of a half-range problem in [0,U] is also part of a larger set that is complete in the full-range [ −U,U], a full-range boundary condition is introduced for solving the half-range problem. Specifically, this condition expresses the solution at the boundary valid for allu ε [ −U,U] as the sum of a given forward component inu ε [0,U] and the unknown backward component inu ε [ −U, 0). Thus the basically ill-posed nature of the half-range problem, viz., that is required to find the response in [ —U,U] from given data in [0,U], is formulated over the entire domain at the boundary as compared to the usual approach that expresses the boundary condition only over [0,U]. This allows us, through a two-step process that considers the full-range properties of the eigenfunctions in [ —U,U] only, to obtainnumerically exact extrapolated end-point and CaseX-function. This means, because of the relationship of these fundamental half-range data with standard half-range expansion coefficientsa 0+ andA(v) [2], that the transient integral of the half-range solution has been reduced to mechanical quadratures.
Materialart:
Digitale Medien
URL:
http://dx.doi.org/10.1007/BF00952255
Permalink
