High accuracy power series method for solving scalar, vector, and inhomogeneous nonlinear Schrödinger equations

We develop a high accuracy power series method for solving partial differential equations with emphasis on the nonlinear Schrödinger equations. The and computing speed can be systematically arbitrarily increased to orders of magnitude larger than those other methods. Machine precision easily reached sustained long evolution times within rather short time. In-depth analysis characterisation all sources error are performed by comparing numerical solutions exact analytical ones. Exact approximate boundary conditions considered shown minimise errors finite background. is extended cases external potentials coupled