Variable-step-size corrector formula

Coefficients for Use in Variable-Step-Size Corrector Formula [Eq. (3.20)], as Reported by... 

Many predictor-corrector formulas are available. The original implementation of the GDI method suggested a set of constant step-size formulas of order that increased as the integration proceeded. We agree with the assessment of Escobedo and de Pablo [49] that lower-order schemes should be preferred because they are more stable, are easier to implement with a variable step size, and do not compromise accuracy—in most cases it is the uncertainty in the simulation averages that limits the overall accuracy of the integration. Escobedo and de Pablo present two second-order corrector formulas that allow for a variable step size. Both are of the form [49]... 

MATLAB has two new stiff integration routines. These are ode 15s and ode23s. The routine odelSs is a variable order (up to order 5) and a variable step size program that is based upon the Klopfenstein modification of classical backward difference formulas called numerical differential formulas (Klopfenstein, 1971). Standard backward difference formulas are also available as an option. In order to determine optimum step size and speed convergence of the implicit corrector formulas, the method depends upon the Jacobian, J, of the derivative function / in... 

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