We describe a method for removing the numerical errors in the modeling of linear evolution equations that are caused by approximating the time derivative by a finite difference operator. The method is based on integral transforms realized as certain Fourier integral operators, called time dispersion transforms, and we prove that, under an assumption about the frequency content, it yields a solution with correct evolution throughout the entire lifespan. We demonstrate the method on a model equation as well as on the simulation of elastic and viscoelastic wave propagation.

翻译：我们描述一种方法来消除线性进化方程式模型模型的数值错误,这种错误是由一个有限差分操作员接近时间衍生物造成的。这种方法基于某些Fourier整体操作员所实现的整体变异,称为时间分散变异,我们证明,根据对频率内容的假设,它产生一种在整个寿命期内正确演化的解决方案。我们用模型方程式以及弹性和粘结波波传播的模拟来演示该方法。