  Recently there has been a growing interest in computational methods for
quantum scattering equations that avoid the traditional decomposition of wave
functions and scattering amplitudes into partial waves.The aim of the present
work is to show that the weighted-residual approach in combination with local
basis functions give rise to convenient computational schemes for the solution
of the multi-variable integral equations without the partial wave expansion.The
weighted-residual approach provides a unifying framework for various
variational and degenerate-kernel methods for integral equations of scattering
theory. Using a direct-product basis of localized quadratic interpolation
polynomials,Galerkin, collocation and Schwinger variational realizations of the
weighted-residual approach have been implemented for a model potential. It is
demonstrated that, for a given expansion basis, Schwinger variational method
exhibits better convergence with basis size than Galerkin and collocation
methods. A novel hybrid-collocation method is implemented with promising
results as well.
