Numerical Solutions of the One-Dimensional Primitive Equations Using Galerkin Approximations With localized Basis Functions

The Galerkin method is applied to a pair of linear and then nonlinear primitive (wave) equations. This results in a system of ordinary differential equations. Procedures are included for generating the coefficient matrices of the system of ordinary differential equations when piecewise Hermite cubic functions are used as basis functions. It is demonstrated that this system can be efficiently solved by an implicit method. Numerical examples show that integration using the Galerkin method is more efficient than the corresponding finite-difference method with central differences in space.