A computational approach for the engineering analysis of ablative-type thermal protection systems (TPS) in atmospheric reentry ballistic flights is communicated. We first propose an improved lumped differential approach for ablative thermal protection analysis, which involves the use of materials with low thermal diffusivity. The results obtained for a one-dimensional thermal ablation problem in a finite slab are compared against those obtained by previously reported lumped differential solutions. Benchmark results for the local nonlinear model, obtained through the generalized integral transform technique, are utilized to verify the proposed solution in a realistic ablation problem, consisting of a low thermal diffusivity material subjected to a prescribed net aerodynamic heating. In addition, an integrated symbolic-numerical system is constructed based on the Mathematica platform for the derivation and computation of all the related quantities along the flight, yielding the transient behavior of the TPS recession and thermal performance for both the constant and variable initial thickness along the vehicle nose region. An illustrative example of the computational tool and the typical results for an orbital platform in ballistic reentry flight are presented.