Dr. Zhu presented a talk on the use of local time steps in solving systems of equations. He began his talk with by explaining how stepping works with initial value problems (IVP) when using explicit and implicit methods and for boundary value problems. Dr. Zhu explained that in attempt to make sure that the numerical solutions are stable and accurate, the time steps used in solving the equations are often too small and unnecessary.

Dr. Zhu and his team have been researching the use different time steps at different spatial points in the process. The diagrams used by Dr. Zhu presented a clear under standing of what they are studying. His first example was demonstrating his technique for reaction-diffusion equations with linear diffusion terms where he showed the use of different time steps maintained the order of accuracy.

Local time stepping may be applied to implicit methods such as Crank-Nicolson Method and Newton's Method, methods using block matrices and to nonlinear algebraic equations.

The current research results show improvements when using local stepping as opposed to the uniform step method. Efficient and accurate results have been provided for both implicit and explicit methods. More research is need for solving nonlinear systems of equations.