Reducing the truncation error in Taylor model multiplication

We present two new methods, a simple fast and a slower more precise one, to reduce the truncation error occurring during multiplication in verified Taylor model arithmetic. These methods were implemented in MATLAB in INTLAB’s Taylor model toolbox which targets solving ordinary differential equations rigorously, i.e., numerical solutions are computed along with rigorous error bounds that include all numerical as well as all rounding errors so that the exact solution must lie within these error bounds. The methods are applied to several test cases to show their effect.