The variable step Adam's method is shown to be stable for any order changing scheme. The Nordsieck form of Adam's method, however, is shown to be stable only if the step size and order are fixed for p steps following a change to an r-step method, where p is r or r+1 depending on the algorithm used to interpolate the necessary higher derivatives. Finally, general consistent and strongly, stable multistep and multivalued methods are shown to be stable if the method is fixed for a certain number of steps following each method change and step size changes are small. This number is independent of the differential equation and the step sizes.
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