From series expansions to exact solutions
by Dr Iwan Jensen
Abstract: Recently we have been able to find numerically the exact solutions for a number of lattice polygon models. In all cases we start by calculating an exact series expansion for the problem at hand and we then proceed to find the exact solution. In the simplest cases this is done via an educated guess of the form of the solution leaving only some polynomials to be determined. In more complicated cases we find
solutions in the form of high order linear ODEs. In one particular instance we are able to find a closed form solution to a problem involving a 4th order ODE.
In this talk I will briefly outline why we study these problems, how we calculate the series and find the exact solutions and discuss what we have learned.
This is joint work (in part) with Tony Guttmann and Christoph Richard.
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