We interpret the Cayley transform of linear ( niteor in nitedimensional) state space systems as a numerical integration scheme of Crank Nicolson type. The scheme is known as Tustin's method in the engineering literature, and it has the following important Hamiltonian integrator property: if Tustin's method is applied to a conservative (continuous time) linear system, then the resulting (discret...

We interpret the Cayley transform of linear (finiteor infinite-dimensional) state space systems as a numerical integration scheme of Crank–Nicolson type. The scheme is known as Tustin’s method in the engineering literature, and it has the following important Hamiltonian integrator property: if Tustin’s method is applied to a conservative (continuous time) linear system, then the resulting (disc...

We present a novel numerical method and algorithm for the solution of the 3D axially symmetric timedependent Schrödinger equation in cylindrical coordinates, involving singular Coulomb potential terms besides a smooth time-dependent potential. We use fourth order finite difference real space discretization, with special formulae for the arising Neumann and Robin boundary conditions along the sy...

<p style='text-indent:20px;'>We consider a hyperbolic free boundary problem by means of minimizing time discretized functionals Crank-Nicolson type. The feature this functional is that it enjoys energy conservation in the absence boundaries, which an essential property for numerical calculations. existence and regularity minimizers shown estimate derived. These results are then used to sh...

Abstract. This article is devoted to the study of the finite element approximation for a nonlocal nonlinear parabolic problem. Using a linearised Crank-Nicolson Galerkin finite element method for a nonlinear reaction-diffusion equation, we establish the convergence and error bound for the fully discrete scheme. Moreover, important results on exponential decay and vanishing of the solutions in f...