Operator-splitting methods respecting Eigenvalue problems for convection-diffusion and wave equations

We discuss iterative operator splitting method for wave-equations motivated from the eigenvalue-problem to decide the splitting process. The operator-splitting methods are wel-know to solve such complicated multidimensional and multi physics problems. Often it is not good understood how to decouple the underlying operators. We propose a method based on computing the eigenvalues for the simpler problem to decide the splitting operators and the time-steps. We present the analysis and the numerical results