Seventh order hybrid block method for solution of first order stiff systems of initial value problems

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Department of Mathematics, University of Lagos Akoka, Lagos, Nigeria

Abstract

A hybrid second derivative three-step method of order 7 is proposed for solving first
order stiff differential equations. The complementary and main methods are generated
from a single continuous scheme through interpolation and collocation procedures.
The continuous scheme makes it easy to interpolate at off-grid and grid points. The
consistency, stability, and convergence properties of the block formula are presented.
The hybrid second derivative block backward differentiation formula is concurrently
applied to the first order stiff systems to generate the numerical solution that do not
coincide in time over a given interval. The numerical results show that the new method
compares favorably with some known methods in the literature.

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