EFFICIENT AND PARALLEL SOLUTION OF HIGH-ORDER CONTINUOUS TIME GALERKIN FOR DISSIPATIVE AND WAVE PROPAGATION PROBLEMS

We propose efficient and parallel algorithms for the implementation of the high-order continuous time Galerkin method for dissipative and wave propagation problems. By using Legendre polynomials as shape functions, we obtain a special structure of the stiffness matrix that allows us to extend the diagonal Pade'\ approximation to solve ordinary differential equations with source terms. The unconditional stability, hp error estimates, and hp superconvergence at the nodes of the continuous time Galerkin method are proved. Numerical examples confirm our theoretical results.