A model for the propagation of rounding error in a Klein-Gordon equation (Q1825015)

Modern powerful computers do help in the extensive numerical investigations of important problems in various sciences and technologies. Models are built and implemented particularly with the relevant error analysis largely improved. The authors show that rounding errors seriously affect the finite difference solutions of a parametrically driven Klein-Gordon equation. Propagation of rounding errors in long time calculations and instabilities are discussed. Discrete operator, multiple scales together with the appropriate numerical analysis and the overall advantages of the perturbation approach are also dealt with in detail.