A numerical tour of wave propagation |

Take

for an example. Using the 2nd-order approximation in Eq. (31), we expand it at the time and the point

(41) |

That is to say,

(42) |

At time and , we expand

as

(43) |

Thus, we have

(44) |

In summary,

(45) |

If we define:

(46) |

we can easily find that is a good approximation of up to 2nd order, allowing for the 2nd order Pade expansion:

(47) |

Then, we have

(48) |

A numerical tour of wave propagation |

2021-08-31