M.S.

An accuracy study is made of central finite difference methods for solving boundary value problems which are governed by second order differential equations with variable coefficients leading to odd order derivatives. Three methods are studied through applications to selected problems. Definitive expressions for the error in each method are obtained by using Taylor series to derive the differential equations which exactly represent the finite difference approximations. The resulting differential equations are accurately solved by a perturbation technique which yields the error directly. A half station method, which corresponds to making finite difference approximations before expanding derivatives of function products in the differential equations, was found superior to two whole station methods which correspond to expanding such products first. / M.S.