Construction of the Nordsieck second derivative methods with RK stability for stiff ODEs

In this paper, we study the construction and implementation of special Nordsieck second derivative general linear methods of order p and stage order in which the number of input and output values is rather than . We will construct A- and L-stable methods of orders three and four in this form with Runge-Kutta stability properties. The efficiency of the constructed methods and reliability of the proposed error estimates are shown by implementing of the methods in a variable stepsize environment on some well-known stiff problems.