A Family of Nested General Linear Methods for Solving Ordinary Differential Equations

General linear methods (GLMs) was introduced as a generalization of Runge{Kutta (RKMs) and multistep (LMMs). The discovery general method gave insight into the new that are neither RKMs or LMMs. Here, classes GLMs nested in their stages mono-implicit output presented, these referred to (NGLMs). Procedures for deriving members algebraically stable discussed herein NGLMs have been derived up order p = 5. Implementation procedure which include solution non-linear systems equations by simplified Newton iterations step size changing strategy discussed. 3 NGLM has implemented on two test problems variable size, results compared with MATLAB ode15s RADAU IIA.