Symmetrization of the Sinc-Galerkin Method with Block Techniques for Elliptic Equations

The discrete system for the symmetric Smc-Galerkin method applied to the self-adjoint, elliptic partial differential equation is extremely sparse (though not banded in the classical sense). Its highly ordered structure can be advantageously used in numerical computations. Efficient block techniques for this symmetric discrete system are described and the numerical results are compared to the standard Sinc-Galerkin method (for which the discrete system is non-symmetric). These two different Sinc-Galerkin methods arise from different choices of the weight function for the Galerkin inner products. For both Sinc-Galerkin methods described, when there are 2M + 1 basis functions, the same exp (-K√M), K > 0, convergence rate occurs. The symmetric Sinc-Galerkin method can be further improved by adroit parameter selections which are described. Numerical results substantiate the improvement due to these parameter choices.