In this paper, we state and prove the conditions for the non-singularity of the <em>D</em> matrix used in deriving the continuous form of the Two-step Butcher’s hybrid scheme and from it the discrete form...In this paper, we state and prove the conditions for the non-singularity of the <em>D</em> matrix used in deriving the continuous form of the Two-step Butcher’s hybrid scheme and from it the discrete forms are deduced. We also show that the discrete scheme gives outstanding results for the solution of stiff and non-stiff initial value problems than the 5<sup>th</sup> order Butcher’s algorithm in predictor-corrector form.展开更多
文摘In this paper, we state and prove the conditions for the non-singularity of the <em>D</em> matrix used in deriving the continuous form of the Two-step Butcher’s hybrid scheme and from it the discrete forms are deduced. We also show that the discrete scheme gives outstanding results for the solution of stiff and non-stiff initial value problems than the 5<sup>th</sup> order Butcher’s algorithm in predictor-corrector form.
