A Critical Evaluation of the Resolution Properties of B-Spline and Compact Finite Difference Methods

Resolution properties of B-spline and compact finite difference schemes are compared using Fourier analysis in periodic domains, and tests based on solution of the wave and heat equations in finite domains, with uniform and nonuniform grids. Results show that compact finite difference schemes have a higher convergence rate and in some cases better resolution. However, B-spline schemes have a more straightforward and robust formulation, particularly near boundaries on nonuniform meshes.