Abstract
Equations describing dynamic problems, after spatial discretization by using the finite element or spectral element method, lead to solve large systems of ODE in time. A family of new time integration algorithms based on an iterative time-stepping (ITS) approach is proposed for solving these systems. The method is developed for first-and second-order differential equations, and applied, in particular, to wave equation. It is an implicit time marching method in which, at each time-step, the solution is computed by a fixed-point scheme. The analysis show that the method is accurate, unconditionally stable and that it allows for efficient and parallel implementations because no matrix inversion is required and only matrix-vector multiplications and vector scaling operations are involved.
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