A method of estimating error for certain wave guide problems

A particular integral equation of the first mode which can be obtained for a certain class of rectangular waveguide joints is examined. Based on an example of an equation for a joint with fine screens, a method of constructing a reciprical operator is described. It is shown that a proof of the existence of a solution to a basic equation can be reduced to a proof of the existence of a solution to a small set of heterogeneous linear algebraic equations. A method of estimating error of an approximate solution and estimating error of linear functions from that solution which define the coefficients of reflection is presented. A good estimation of a functional value is obtained using this method.