An Examination of Precision Effects on Numerical Solutions of Partial Differential Equations
Presented at IIT SIAM 2011.
Abstract: We demonstrate massively parallel scaling of solutions to the three dimensional nonlinear Schrodinger equation. In doing so we find that numerical precision effects determine the accuracy to which numerical solutions can be obtained. We then examine numerical precision effects more closely for the Sine-Gordon equation. We implement high order implicit Runge Kutta solvers using fixed-point iteration and compare diagonally and fully implicit schemes. We find that in quadruple precision, fourteenth order time stepping schemes are very efficient.