The Sinc-Galerkin method for parameter-dependent self-adjoint problems

摘要

The Sinc-Galerkin method is being applied to a growing number of diverse problems in ordinary and partial differential equations including both forward and inverse (parameter recovery) problems. As a result of these continuing extensions, the treatment of parameter-dependent problems needs to be thoroughly investigated. Two specific questions considered here are the incorporation of various nonhomogeneous boundary conditions and the treatment of a variable parameter. The latter topic is particularly important for inverse problems that arise when numerically estimating physical parameters. The point of view taken emphasizes the maintenance of the classical exponential convergence rate. The techniques described are suitable both for the direct problem and for the parameter estimation problem. Numerical results are presented to substantiate the accuracy of the method.