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BLOCK METHOD FOR NUMERICAL INTEGRATION OF INITIAL VALUE PROBLEMS IN ORDINARY DIFFERENTIAL EQUATIONS

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May 9, 2020 No Comments ›› Sunday

BLOCK METHOD FOR NUMERICAL INTEGRATION OF INITIAL VALUE PROBLEMS IN ORDINARY DIFFERENTIAL EQUATIONS

ABSTRACT

A self starting six step ten order block method with three off-grids points have been derived for solving Ordinary Differential Equations (ODE) using interpolation and collocation procedures. Multiple numerical integrators were arrived at. These integrators are combined into a single block matrix equations. Our method was found to be zero stable, consistent  and convergent. The numerical examples considered showed that our method gave better accuracy than some existing methods. The stability analysis shows that our method is A-stable and of order 10.

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