Exponentially fitted third derivative three-step methods for numerical integration of stiff initial value problems

In this paper, we consider the construction of exponentially fitted third derivative three-step method of order six for the numerical integration of stiff initial-value problems. The numerical analysis of the stability of the new method was discussed and some numerical experiments confirming theoretical expectation are provided. Finally, the numerical results show that the new method is A-stable and compete favorably with the existing methods in terms of efficiency and accuracy.