Solving equations by successive substitution: The problems of divergence and slow convergence

Eberhart, J. G.

doi:10.1021/ed063p576

Cited by 11 publications

(2 citation statements)

References 3 publications

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“…Knowing the boundaries of the "permitted" interval for α may be helpful when trying to solve 3 rd -degree equation (3) for α by means of the interval-bisection method (Mukesh, 1988), or by an iterative method (Eberhart, 1986), choosing from the same interval the firstguess value 1 α , needed to start the iterative calculations. By employing either method, we found the α values at equilibrium reported in the 5th column of the On the other hand, we know that, at equilibrium, α can never be 0, so that, for , α must tend asymptotically to a limiting value, as actually given by formula (4).…”

Section: Main Findings and Some Implicationsmentioning

confidence: 99%

Gaseous Equilibria: Some Overlooked Aspects

Giomini

Marrosu

Cardinali

et al. 2000

Chem. Educ. Res. Pract.

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For some gaseous equilibria, with particular stoichiometric characteristics, the addition of some reactant or products, as large as it may be, when operated under constant temperature and pressure, cannot cause a (practically) complete shift of the equilibrium to the right, or to the left. The effect of the addition is counteracted by the increase of volume that the system undergoes to keep constant the pressure. [Chem.

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Section: Main Findings and Some Implicationsmentioning

confidence: 99%

Gaseous Equilibria: Some Overlooked Aspects

Giomini

Marrosu

Cardinali

et al. 2000

Chem. Educ. Res. Pract.

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show abstract

“…Some examples are provided here of nonlinear equations or systems of equations that can be solved by the method of successive substitution. Of course, other numerical methods also can be used (13,14).…”

Section: Summary and Commentsmentioning

confidence: 99%