Project Coral


Welcome to the wiki page of

Project Coral
Exponential quadrature

coordinated by Marlis Hochbruck (Karlsruhe).

The group members are:

  • Ghasem Abbasi (Tehran)
  • Gábor Csörgő (Budapest)
  • Hicham El Boujaoui (Marrakesh)
  • Hatice Tavli (Chemniz)

The project description can be downloaded from here.

Discussion of Project Coral.


The aim of this project is to study the numerical approximation to solutions of linear abstract differential equations

u'(t) + Au(t) = f(t),u(t0 + ) = u0

on a Banach space X by exponential quadrature formulas.

To define such quadrature formulas we choose non-confluent collocation nodes c,...,cs and define approximations 0ad854578577b4ad978e361e7e5a6dd7.png, where tn = t0 + nh, n = 0,1,... via


with weights


Here, lj is the Lagrange interpolation polynomial


The project involves

  • construction of exponential quadrature formulas
  • convergence analysis in different Banach spaces (e.g. in Lp) and with different boundary conditions
  • numerical experiments (using Matlab or any other programming language)


  1. M. Hochbruck, A. Ostermann: Exponential Runge-Kutta methods for parabolic problems, Appl. Numer.
  2. Math., vol. 53, no. 2-4, pp. 323-339 (2005)
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