  A multidomain spectral approach for Painlev\'e transcendents on unbounded
domains is presented. This method is designed to study solutions determined
uniquely by a, possibly divergent, asymptotic series valid near infinity in a
sector and approximates the solution on straight lines lying entirely within
said sector without the need of evaluating truncations of the series at any
finite point. The accuracy of the method is illustrated for the example of the
tritronqu\'ee solution to the Painlev\'e I equation.
