# Removing numerical dispersion from linear evolution equations

## TL;DR

This paper introduces a novel method using Fourier integral operators to eliminate numerical dispersion errors in linear evolution equations, improving the accuracy of simulations over time.

## Contribution

It presents a new approach employing time dispersion transforms to correct numerical errors caused by finite difference approximations in linear evolution equations.

## Key findings

- The method effectively removes numerical dispersion in model equations.
- It improves the accuracy of elastic and viscoelastic wave simulations.
- The approach maintains correct evolution throughout the entire simulation lifespan.

## Abstract

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.