Genre: Information/Explanation

Nature of problem : With the present program the derivation of the coefficients produced by the equation ( 14 ) is obtained . The first part of the proposed program consists of the calculation of the matrix elements which form the coefficients of the system of equations . The second part of the proposed program , as this has been explained in [ 1 ] , [ 2 ] and [ 3 ] , consists of the iterative application of the L ' Hospital's rule ( to avoid coefficients of the form 0 / 0 ) for the computation of the solution of these equations that make up the coefficients of the method ( 14 ) . We note that the system of equations produced by the equation ( 14 ) is solved by an application of Cramer's rule . The above procedure is repeated for the calculation of the coefficients of the methods ( 24 ) - ( 25 ) and for the methods ( 28 ) - ( 29 ) . Solution method : Symbolic computation using Maple . Running time : 1800 seconds References : [ 1 ] T. Lyche , Chebyshevian multistep methods for ordinary differential equations , Numerische Mathematik , 10 ( 1972 ) 65-75 . [ 2 ] A.D. Raptis , Exponential multistep methods for ordinary differential equations , Bulletin of the Greek Mathematical Society , 25 ( 1984 ) 113-126 . [ 3 ] T.E. Simos , Numerical solution of ordinary differential equations with periodical solution . Doctoral Dissertation , National Technical University of Athens , 1990 .