Numerical Spectral Solvers for Differential and Integral Equations

Marco Heinen

Physical engineering department, Division of Science and Engineering of the University of Guanajuato, Mexico


In this course we are going to study state-of-the-art numerical techniques for the solution of differential, integral and integro-differential equations with focus on the Schrödinger equation for single quantum-mechanical particles and the Ornstein-Zernike equation for the correlation functions of classical particles in dense fluid phases. We will study in detail the advantages of using numerical grids with exponentially increasing grid spaces [Talman1978, Hamilton2000] in spectral methods. The implementation of fast and strongly convergent fixed-point solvers [Heinen2014] will be discussed in detail, and the performance of various numerical codes will be demonstrated in class.



  1. [Talman1978] …........“Numerical Fourier and Bessel Transforms in Logarithmic Variables”, J. Comput. Phys. 29, 35-48 (1978)
  2. [Hamilton2000] ….....“FFTLog”, Mon. Not. R. Astron. Soc., 312, 257 (2000)
  3. [Heinen2014] …........ "Highly asymmetric electrolytes in the primitive model: Hypernetted chain solution in arbitrary spatial dimensions”, J. Comput. Chem. 35, 275-289 (2014).


Summary of academic career

Prof. Marco Heinen studied physics at RWTH Aachen University (Germany). Your main research interest concerns the statistical physics of soft matter systems, which he study by computer simulations and semianalytical, numerical methods. In the year 2011 he obtained your Doctor of Science degree from the Heinrich-Heine University Düsseldorf (Germany) with the thesis project conducted at the Research Center Jülich (Germany). Your doctoral thesis has the title “Charged colloids and proteins: Structure, diffusion an rheology”. From 2012 until 2014 he was a PostDoc at the Heinrich-Heine University Düsseldorf, in Prof. Hartmut Löwen's Theoretical Physics group. Your second PostDoc appointment (from 2014 until 2016) was at the California Institute of Technology (Caltech, Pasadena, CA), in Prof. John F. Brady's Chemical Engineering group. Since March 2016 he is associate Professor at the Division of Science and Engineering of the University of Guanajuato, Mexico.