Using Polynomial Regression in Designing the Time Filters for the Leapfrog Time-Stepping Scheme

A general framework is presented based on the least squares polynomial regression to design time filters for the leapfrog time-stepping scheme with required amplitude and phase properties. The well-known Robert–Asselin filter and its modification, the Robert–Asselin–Williams filter, are obtained using the zeroth-degree and first-degree polynomial regression, respectively. It is shown that using the second-degree polynomial regression, one can achieve seventh-order amplitude accuracy with only four time levels. In addition, the designed filter exhibits promising results when used with a semi-implicit time-stepping scheme.