Convergence of Padé Kernel Approximants to the Delayed Dirac Function
Abstract
We derive from the solutions of Kummer's equation an expression for the exponential function, which when restricted to integer parameters gives the [M, N] Padé approximation and its error. Laplace inversion, using Bromwich's integral, then yields an approximation of the form
Formula
to δ(λ − t) the delayed Dirac kernel, in which the constants {αi, v, Ki,v: i = 1, 2 , …,N, ν = M − N + 1} are those of the partial fraction decomposition of the [M, N] Padé approximation. These constants also occur in direct quadrature formulae to invert Laplace transforms. Finally, we show that the kernel approximants converge for λ > t.
URI
http://imamat.oxfordjournals.org/content/25/1/17.shorthttp://erepository.uonbi.ac.ke:8080/xmlui/handle/123456789/37111
Citation
IMA J Appl Math (1980) 25 (1): 17-27Publisher
University of Nairobi. Department of Mathematics