On the nonlinearity of HBDF based methods in solutions of IVPs

For the numerical solutions of stiff systems of ODEs and PDEs, multistep methods based on HBDFs can be used. For all types of the methods, there is at least one stage equation together with main equation in which BDF methods used by considering off-step points in order to make the considered stage equations. Since, the test problems are often nonlinear and on the other hand, the solver of that problem can also be nonlinear, hence, in this work, the nonlinearity of the solving methods will be illustrated and also compared regarding to the number of stage equations of the HBDF based methods.