Exponentially Convergent Parallel Discretization Methods for the First Order Evolution Equations

By Ivan P. Gavrilyuk, V. Makarov. 2001

63 citations recorded by the source corpus.

Abstract We propose a new discretization of an initial value problem for differen- tial equations of the first order in a Banach space with a strongly P-positive operator coefficient. Using the strong positiveness, we represent the solution as a Dunford- Cauchy integral along a parabola in the right half of the complex plane, then transform it into real integrals over (−∞,∞), and finally apply an exponentially convergent Sinc quadrature formula to this integral. The integrand values are the solutions of a finite set of elliptic problems with complex coefficients, which are independent and may be solved in parallel.

Subfields: Modeling and Simulation, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/48425759f901e0615d0f220810011467dd9964f7

Citations in the corpus

• The Exponentially Convergent Trapezoidal Rule (2014, unknown): “Relevant papers include [56, 81, 180, 181] (parabolic contours), [105, 121, 148, 181] (hyperbolic contours), and [38, 171] (Talbot contours).”