Hybrid block formulae whose eigenvalues of Jacobian matrices are close to the imaginary axis of the complex plane

Methods for integrating stiff initial value problems are required to be A-stable. Of great interest are A-stable methods whose Jacobian matrices have their eigenvalues close to the imaginary axis of the complex plane. This class of A-stable methods are very rare. This paper is on the development of a new family of A-stable hybrid block method whose Jacobian matrices possess eigenvalues on the imaginary of the complex plane via interpolation and collocation techniques. The family of methods developed herein are A-stable for order p ≤ 18. Numerical solutions generated by the new method are compared with existing methods in the literature. The numerical results show that the new class of methods are more efficient and accurate.