Ritz Method Corresponding to a Point Force in the Interior of the Domain

As, before, choose an N -term approximation to the solution u (equation 3.8) containing the unknown coefficients and the known function . The known functions must be linearly independent and must satisfy the condition = 0 at x = 0. In Ritz method, the solution is obtained by extremising the variational functional I , i.e. by setting the first variation to zero. Substituting the expressions for u and its variation in the expression (3.52) for and setting it to zero, we get the same algebraic equations as before (equation 3.15). Further, the coefficient matrix of these equations is the same as before (equation 3.13) but the right side vector contains an additional term compared to equation (3.14). Thus, is given by

(3.53)