Derivation And Numerical Analysis of Implicit Time Stepping Schemes

Chu, Chunlei (ConocoPhillips) | Stoffa, Paul L. (The University of Texas at Austin)

OnePetro 

We demonstrate that implicit time integration methods for second-order-in-time wave equations can be derived from rational expansions to the cosine function of pseudo-differential operators. Using the scalar wave equation as an example, we give complete stability condition and grid dispersion analysis results for general implicit time integration methods. Furthermore, we propose an optimization method to develop unconditionally stable implicit time stepping schemes.