Research Areas
Asymptotic Analysis

Many models in applied mathematics are far too complex to be solved exactly with a nice, neat, closed-form solution. Computer generated numerical solutions can be useful, but do not offer an easy way to generalize or analyze the behavior of the system over a range of parameter values.

An alternative strategy is to derive an approximate solution. In fact, asymptotic and perturbation methods employ the presence of a small parameter in the problem, e.g., a small coefficient in the differential equation, to derive an approximate solution of the model. We use asymptotic and perturbation methods in many applied problems and also develop new methods.