A New Sinc-Galerkin Method for Convection-Diffusion Equations with Mixed Boundary Conditions

摘要

A new sinc-Galerkin method is developed for approximating the solution of convection-diffusion equations with mixed boundary conditions on half-infinite intervals. The method avoids differentiation of the coefficients of the PDE, rendering it appropriate as a forward solver in an inverse coefficient problem. The method has the advantage that no functions are appended to the sine basis in the discretization. An error analysis is included, and it is shown that the error in the approximate solution is bounded in the infinity norm by the norm of the inverse of the coefficient matrix multiplied by a factor that decays exponentially with the size of the system. We demonstrate the exponential convergence of the method on several test problems.