Year: 1997
Type: article
Abstract: A collocation procedure is developed for the initial value problem $u’(t) = f(t,u(t))$, $u(0) = 0$, using the globally defined sinc basis functions. It is shown that this sinc procedure converges to the solution at an exponential rate, i.e., $\mathcal { O} (M^{2} \exp (-\kappa \sqrt {M}) )$ where $\kappa > 0$ and $2M$ basis functions are used in the expansion. Problems on the domains $\mathbb {R} = (-\infty ,\infty )$ and $\mathbb {R} ^{+} = (0,\infty )$ are used to illustrate the implementation and accuracy of the procedure.
Source: Mathematics of Computation
Authors: Timothy S. Carlson, Jack Dockery, John Lund
Institutions: Santa Fe Institute, Montana State University
Language: English
Subfield: Numerical Analysis
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W2016558594