Topics for Master-thesis projects

• Fractal derivatives (analysis, numerics, applications)
  
  
• Fractional derivatives (analysis, numerics, applications)
  
  
• Boundary-value methods (ODE and PDE time-integration)
  
  
• Matrix-Newton methods (numerical analysis)
  
  
• Continuous Newton-methods (analysis and experiments)
  
  
• Holistic discretizations of partial differential equations
  
  
• Theory of the homotopy analysis method (convergence, h-curve)
  
  
• Adaptive grids in four dimensions
  
  
• Matrix-Newton differential equations
  
  
• Travelling waves in higher-order PDE models
  
  
• Nonstandard finite differences for nonstandard differential equations
  
  
• Supraconvergence in adaptive grid methods
  
  
• Traffic flow models: adaptive grids in a network of roads
  
  
• Stability of travelling waves via the Evans function
  
  
• Multiplicity of solutions of nonlinear boundary-value problems