Abstract. In this paper, we consider the development and implementation of algorithms for the solution of stiff first order initial value problems. Method of interpolation and collocation of basis function to give system of nonlinear equations which is solved for the unknown parameters to give a continuous scheme that is evaluated at selected grid points to give discrete methods. The stability properties of the method is verified and numerical experiments show that the new method is efficient in handling stiff problems.

We introduce one step continuous Runge Kutta collocation method with three free parameters for the solution of stiff first order ordinary differential equations. We adopt interpolation and collocation of the approximate solution at some selected grid points to give system of non linear equations. Using Crammer's rule to solve for the unknown parameters and substituting into the approximate solution gives the continuous method. To determine how best to fix the free parameters, we consider