This chapter presents the theory of homogeneous difference schemes for the solution of equations with variable coefficients

k ( x ) ctx

A special attention is being paid to various forms of homogeneous difference schemes and their approximation and convergence for discontinuous coefficients k, q and / as well as for non-equidistant grids. Not much is known in such cases. Later in this chapter we will survey some devices that can be used to obtain simpler forms and higher orders.