Exponentially convergent parallel discretization methods for the first order evolution equations (Q2781173)

A new discretization of an initial value problem for first order differential equations in a Banach space with a strongly \(P\)-positive operator coefficient is proposed. Using the strong positiveness, the solution is represented as a Dunford-Cauchy integral along a parabola in the right half of the complex plane. Then it is transformed into a real integral. Finally, the authors apply an exponentially convergent Sinc quadrature formula to this integral. The values of the integrand are the solutions of a finite set of elliptic problems with complex coefficients, which are independent and may be solved in parallel.