This paper is concerned with the efficient computational implementation of combustion chemistry, for use in PDF methods and other applications. A new method of coupling reactions and mixing processes based on manifold points with detailed chemistry is developed. Investigations are made of three different kinds of methods: the direct numerical integration of the coupled reaction and mixing equations; the direct numerical integration of the equations obtained by using operator-splitting to split reaction and mixing; and the new method--solving the split system based on manifold points with detailed chemical kinetics. Errors between the solutions are studied. It is found that chemical reactions have a significant influence on the accuracy of operator-splitting methods. The solution of the split systems based on manifold points provides an accurate representation for the solution of the full coupled equations. This means that tabulations can be made on manifolds with no simplification made to the chemistry.