Oey, L-Y., 1982: Implicit schemes for differential equations. Journal of Computational Physics, 45, 443-468.

Abstract: Implicit high-order accurate temporal-integration schemes are developed to reduce partial differential equations of evolution type to a sequence of ordinary differential equations involving the spatial directions only. The ordinary differential equations are solved using various accurate integration methods. The schemes are free from extraneous boundary and/or initial conditions and are stable for large Courant number.