A Class of Numerical Methods of High Order for Stiff Problems in Ordinary Differential Equations

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Abstract
A class of A-stable high order integration methods involving second derivatives is developed. A suitable iteration technique is suggested to solve the non-linear systems that arise at each step of the method. The use of this special technique overcomes the disadvantage of second derivatives in our formulae. To obtain starting values for the iteration a class of explicit A-stable methods is constructed. The A-stability of these methods guarantees that the starting values obtained are a good approximation for the iterative process even if an extremely large integration step is used. Calculated results prove the effectiveness of this technique.

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