In this study, we present numerical methods, based on the optimal quadratic spline collocation (OQSC) methods, for solving the shallow water equations (SWEs) in spherical coordinates. The error associated with quadratic spline interpolation is fourth order locally at certain points and third...

Currently in most global meteorological applications, low-order finite difference or finite element methods, or the spectral transform method are used. The spectral transform method, which yields high-order approximations, requires Legendre transforms. The Legendre transforms have a...