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Most block methods in the literature which are implemented in predictor-corrector mode, usually suffer some stability setbacks and this may hinder their implementation on some stiff problems. In this paper, we construct a stiffly stable block second derivative backward differentiation formula with Chebyshev collocation points that is self-starting and is capable of solving stiff problems. The method is applied in block form as a simultaneous numerical integrator over non-overlapping subintervals. The method is proven to possess stiffly stable, A0 stable and A(α) stable properties. Some numerical examples reveal that this class of methods is very promising and are suitable for solving stiff problems.

A STIFFLY STABLE SECOND DERIVATIVE BLOCK MULTISTEP FORMULA WITH CHEBYSHEV COLLOCATION POINTS FOR STIFF PROBLEMS