  The time dependent spectral renormalization (TDSR) method was introduced by
Cole and Musslimani as a novel way to numerically solve initial boundary value
problems. An important and novel aspect of the TDSR scheme is its ability to
incorporate physics in the form of conservation laws or dissipation rate
equations. However, the method was limited to include a single conserved or
dissipative quantity. The present work significantly extends the computational
features of the method with the (i) incorporation of multiple conservation laws
and/or dissipation rate equations, (ii) ability to enforce versatile boundary
conditions, and (iii) higher order time integration strategy. The TDSR method
is applied on several prototypical evolution equations of physical
significance. Examples include the Korteweg-de Vries (KdV), multi-dimensional
nonlinear Schr\"odinger (NLS) and the Allen-Cahn equations.
