The focus of this paper is the application of the Green element method to the solution of boundary value problems for some classes of fourth-order differential equations with positive constant coefficients.

The given problem is transformed into two coupled second-order differential equations, subject to suitable boundary conditions. It is known that second-order boundary value problems can be reduced to integral equations whose kernel is an appropriate Green’s function. Here, the author relies on Green’s second identity to obtain a weak formulation of the problem, and then solves the integral equations by discretizing the domain. Some examples are given to illustrate the method. These examples, however, do not contain odd order derivatives. It is not clear how the author obtains singular integral equations, since the differential equations considered have smooth coefficients (in fact, only constant coefficients).

The bibliography is quite short; there are many useful references addressing the theoretical and numerical aspects of Green’s function that could have been added [1,2].