Topics for Master-thesis projects (2011)

• Holistic discretizations of partial differential equations (analysis and implementation)
  
  
• Adaptive grids in four dimensions (implementation and visualization)
  
  
• Matrix-Newton differential equations (analysis and/or computation)
  
  
• Travelling waves in an extended fourth-order Richards equation from hydrology (analysis and computation)
  
  
• Nonstandard finite differences for nonstandard differential equations (analysis and implementation)
  
  
• Supraconvergence in adaptive grid methods (numerical analysis)
  
  
• Fractional partial differential equations (numerical analysis)
  
  
• Traffic flow models: adaptive grids in a network of roads (implementation, possible internship at company)
  
  
• Patterns in higher order PDEs: higher than 5th-order! (implementing adaptivity + testwork)
  
  
• Blow-up phenomena in the Korteweg-de Vries equations (implementation + testwork)
  
  
• Periodic boundary conditions in the code MGI=Moving-Grid-Interface (implementation + testwork)
  
  
• Stability of travelling waves via the Evans function (analysis + numerics)
  
  
• Boundary-value methods for time-dependent PDEs (analysis + implementation)