Symplectic-orthogonal Legendre Polynomial And Its Application To The Wave Equation

A class of symplectic-orthogonal matrix polynomials is firstly derived based on the classical Legendre polynomials and spectral properties of Hamiltonian operators. More-over, the Legendre Tau method for the Hamiltonian systems arising from wave equation is proposed, and the spectral numerical scheme is obtained. Finally, the energy-preserving of the numerical solution is proved.