An extension of the Kantorovich method

Abstract

An extension of the Kantorovich method is discussed. The suggested method is demonstrated on the torsion problem of a beam of rectangular cross section. It is found that even when the solution is restricted to a one-term approximation, the method generates very good results also for stresses which are obtained as derivatives of the solution. It is shown that the final form of the generated solution is unique and that the convergence of the iterative process is very rapid. The obtained results indicate that the proposed method is a convenient tool to generate close approximate solutions, thus eliminating the arbitrariness in the choice of coordinate functions, which is a serious shortcoming inherent in the Ritz and Galerkin methods.