by I. P. and Makarov Gavrilyuk
Preprint series: 05-02, Reports on Numerical Mathematics
I. P. and Makarov Gavrilyuk
Abstract: An exponentially convergent approximation to the solution of a nonlinear first order differential equation with an operator coefficient in Banach space is proposed. The algorithm is based on an equivalent Volterra integral equation including the operator exponential generated by the operator coefficient.The operator exponential is represented by a Dunford-Cauchy integral along a hyperbola enveloping the spectrum of the operator coefficient and then the integrals involved are approximated using the Chebyshev interpolation and an appropriate Sinc quadrature. Numerical examples are given which confirm theoretical results.
Keywords: nonlinear evolution equation, exponentially convergent algorithms, Sinc-methods