Abstract by Dane Grundvig
High Order Deferred Corrections
We consider scattering wave problems related to the solution of the Helmoltz Equation in polar coordinates. Using a high order boundary condition, we develop a high order interior scheme based on finite difference methods. The method is inspired by Deferred Corrections which involves repeated replacement of truncation errors by previously computed solutions. Advantages of this scheme include high accuracy, sparse easily solved matrix systems, and relatively fast convergence (compared to other finite difference schemes with similar order). Theoretical results on the order obtained by the method are presented as well as validating numerical results for 2nd, 4th and 6th order implementations.