**Topics for Master-thesis projects**

Dr. P.A. Zegeling (supervisor)

- 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