A Modified Multistep Method for the Numerical Integration of Ordinary Differential Equations

Ab.stract. it has been sho~v~, by I)ahlquist [1] that , q~ k step method for the numericet 15 soll~tion of an orditlary differential equation is unstable unless the order is less than /:93 This paper is concerned with a modificati(m t~o the form of the multistep process such ti~r higher orders can be ~ttained. For k.~7 examples of such modified processes of order 2,~:-t :i have been found and these are given in full for k~(i.