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Removing numerical dispersion from linear evolution equations. (English) Zbl 1481.65163

Summary: 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.

MSC:

65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
65N06 Finite difference methods for boundary value problems involving PDEs
65T50 Numerical methods for discrete and fast Fourier transforms
35A22 Transform methods (e.g., integral transforms) applied to PDEs
35Q86 PDEs in connection with geophysics
35S30 Fourier integral operators applied to PDEs
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