A Seventh-order Block Integrator for Solving Stiff Systems

In this paper, an L0- stable Second Derivative Block Integrator of uniform order seven is proposed for the numerical integration of stiff systems, including large stiff systems resulting from semi discretization of Parabolic differential equations. The conven tional 3-step second derivative backward differentiation formula is obtained from a continuous scheme while the additional methods are obtained from the second derivative of the same continuous scheme. All methods are derived via Interpolation and Collocation techniques and assembled into a block scheme. The convergence and stability properties of the block scheme are discussed and the stability region shown. The performance of the scheme as compared to other existing schemes is considered favorable.