A new hybrid method for solving linear-non-linear systems of equations

This paper presents a new method for solving any combination of linear–non-linear equations. The method is based on the separation of linear equations in terms of some selected variables from the non-linear ones. The linear group is solved by means of any method suitable for the linear system. This operation needs no iteration. The non-linear group, however, is solved by an iteration technique based on a new formula using the Taylor series expansion. The method has been described and demonstrated in several examples of analytical systems with very good results. The new method needs the initial approximations for non-linear variables only. This requires far less computation than the Newton–Raphson method. The method also has a very good convergence rate. The proposed method is most beneficial for engineering systems that very often involve a large number of linear equations with limited number of non-linear equations