Some splitting methods for hyperbolic PDEs

摘要

In this work, a new splitting technique is implemented for solving hyperbolic PDEs. As the main result, the new methods preserve the maximum principle unconditionally or with a mild condition on discretization parameters in comparison with well known methods. Damping of numerical solution in time evolution is investigated. For numerical solution of the Burgers' equation, as a nonlinear problem, an iterative method based on the new splitting technique is presented. Efficiency of the new methods is examined via numerical examples. (C) 2019 IMACS. Published by Elsevier B.V. All rights reserved.