The numerical integration scheme for a fast PetrovGalerkin method for solving the generalized airfoil equation
The main purpose of this paper is to give the numerical integration scheme for a fast PetrovGalerkin method for solving the generalized airfoil equation, considered in a recent paper (Cai, J. Complex. 25:420436, 2009). This scheme leads to a fully discrete sparse linear system. We show that it requires a nearly linear computational cost to get this system, and the approximate solution of the resulting linear system preserves the optimal convergent order. Numerical experiments are presented to confirm the theoretical estimates.
the numerical integration scheme a fast petrovgalerkin method the generalized airfoil equation msc 45l10 65b05