ABSTRACT
The well-known Ritz method for finding an approximate solution to partial and ordinary differential equations consists in the following. The unknown function is written as a well-defined expression which must sat isfy boundary conditions and which includes unknown parameters. The expression is then substituted into the integral corresponding to the given differential equation (i.e., the one for which the given equation is the EulerLagrange equation) and the parameters are chosen so as to minimize this integral. In my article [1] I gave a certain development of the Ritz method that consisted in the following: an interpolation expression for the unknown function is constructed so that this function is equal to arbitrary functions on certain straight lines and then one minimizes the integral into which this expression is substituted. Then the partial differential equation turns out to be approximately replaced by a system of ordinary differential equations. The Ritz method and the last method require a great deal of work mainly related to the computation of the integrals obtained. Moreover, in the case of partial differential equations, both methods can be directly applied only to the case of elliptic equations.
