Variable stepsize multivalue collocation methods

When faced with the task of solving stiff problems, highly stable numerical methods are often needed to avoid the phenomenon of order reduction. The purpose of this paper is to construct a family of high order multivalue collocation methods for the numerical solution of stiff problems and implement them in a variable stepsize environment. We construct a sixth order A-stable method with r=m+1, where m and r are the number of internal and external stages, respectively. The implementation issues of such methods in variable stepsize environments including starting procedure, stage predictors, local error estimation and the changing stepsize strategy are discussed. To show the efficiency and capability of constructed methods in solving stiff problems, some fixed and variable stepsize numerical experiments along with the reliability of local error estimation are presented.