Title: Development and Analysis of 3D Non-Split Optimally Stable Lax-Wendroff Type Difference Scheme for Conservation Laws Authors: M. Kucharik ^1, R. Liska* ^1, S. Steinberg ^2, B. Wendroff ^3 Affiliation: ^1 Czech Technical University, Prague, Czech Republic ^2 University of New Mexico, Albuquerque, U.S.A. ^3 Los Alamos National Laboratory, Los Alamos, U.S.A. Abstract: Direct generalization of a 2D non-split optimally stable Lax-Wendroff (LW) type finite difference scheme to 3D is unconditionally unstable. A variation of this scheme is sub-optimally stable. On the other hand the 3D split extension of the 1D optimally stable LW scheme is also optimally stable. We start with this optimally stable 3D split scheme, assume linearity of fluxes and derive a new 3D non-split scheme. As the transformation is linear and stability analysis is done using scalar advection, the new scheme remains optimally stable. The new scheme is second order both for scalar advection and a general non-linear conservation law. Derivation and analysis of the new scheme has involved processing of large complicated formulas on a 3D stencil (basic and staggered) and has heavily relied on computer algebra facilities. Computer algebra tools have been used for scheme transformation, stability analysis, truncation error analysis and modified equation construction.