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Scientific Computing, and Applied and Numerical Differential Equations


  • Daniel Erik Axel Appelo
  • Yingda Cheng
  • Andrew Jason Christlieb
  • Jun Kitagawa
  • Di Liu
  • Keith S Promislow
  • Jianliang Qian
  • Russell Schwab
  • Olga Turanova

The research interests of the Scientific Computing, and Applied and Numerical Differential Equations group encompass modeling, analyzing, and simulating a wide variety of physical systems using techniques from analysis and differential equations, including the development, analysis, and implementation of fast, stable and accurate numerical algorithms for solving systems of differential equations arising in the engineering and natural sciences.

Areas of particular focus include:

  • Optimal transport theory and algorithms
  • The analysis of interacting particle systems, random walks, stochastic optimal control, and games
  • Models in biology, evolutionary biology, and swarming
  • Mutli-physics and multi-scale modeling of stochastic systems arising in biochemical networks and nano-optics
  • Development of models of solvation, minimal molecular surfaces, and ion channels
  • Analysis of vortices in superconductors
  • Network formation in amphiphilic materials with applications to fuel cells, Lithium ion batteries, and polymer solar cells
  • Development and analysis of higher order numerical schemes, including discontinuous Galerkin methods, integral deferred correction, fully Lagrangian schemes with applications to Hamilton-Jacobi equations, kinetic systems, and plasmas
  • Fast numerical methods for high-frequency wave propagation, Hamilton-Jacobi equations, Gaussian beams, traveltime tomography, seismic imaging, medical imaging, and inverse gravimetry


Group members can be contacted at ApNumPDE@math.msu.edu.