We report here on a substantial advance in the development of algorithms for the numerical investigation of tricritical behavior in a two-variable phase diagram. Such a method of analysing series for models with a tricritical point has been an elusive goal for many years in the context of both magnetism and polymer studies. A full review of the physical systems exhibiting tricriticality and previous calculations in both a series and a simulation context has recently been given by Adler and Privman . These authors derived a test series based on a mean-field model with a tricritical behavior which is well understood and has most of the features of ``real'' tricritical points of 2D and 3D systems. We will summarize the features of the model in section II below.
The only reliable method for studying tricritical points from series expansions that has been applied to date is matching high and low temperature series, when available . Some early studies  also used a standard ``slicewise'' Padé method. In Adler and Privman  this method was applied to the ``test'' series of the mean field model. While those features of the Padé approximant approach which can be regarded as signatures of a tricritical point in the phase diagram, and which were noted in the early studies of tricriticality , were identified, it was concluded, that this most straightforward Padé method is not suitable as an accurate and systematic analysis technique. In the present paper we describe our development of a systematic method, based on elaborations of the two-variable partial differential approximant (PDA) techniques used successfully for bicritical points . The analytic solution with PDAs is given in III and the numerical solution in IV. Section V is devoted to concluding remarks.