Optimally accurate operators for partial differential equations

• In this contribution, we generalise the optimally accurate operators proposed and used in the series of studies on the simulation of seismic wave propagation, especially based on Geller & Takeuchi (1995). Although the operators have been mathematically proven more accurate than conventional methods, the demonstration has been made without a recipe ready for different configurations and the theory is complicated using normal-mode theory, which prevents other physics from applying the methods. Here we show that the operators can be systematically obtained for any form of partial differential equations and we show several applications with numerical examples.