Solving ordinary differential equations by generalized Adams methods: properties and implementation techniques

Generalized Adams methods of order 3, 5, 7 and 9 are used to find numerical solutions of initial value problems. The effectiveness of these methods for the treatment of stiff problems is shown on the basis of their attractive properties and an efficient technique to deal with the algebraic nonlinear systems representing the discrete counterpart of the continuous problem. Numerical examples are also presented in which an experimental code based on these methods is compared with two well known codes for ODEs. The numerical results are quite satisfactory and suggest that these methods may have a useful role in the solution of stiff ODEs.