The tt* equation that we will study here is classed as case 4a by Guest et al. in their series of papers Isomomodromy aspects of the tt* equations of Cecotti and Vafa. In their comprehensive works, Guest et al. give a lot of beautiful formulas on and finally achieve a complete picture of asymptotic data, Stokes data and holomorphic data. But, some of their formulas are complicated, lacking of intuitional explanation or other relevant results that could directly support them. In this paper, we will first verify numerically their formulas among the asymptotic data and Stokes data. Then, we will enlarge the solution class assumed by Guest et al. from the Stoke data side. Based on the numerical results, we put forward a conjecture on the enlarged class of solutions. At last, some trial to enlarge the solution class from the asymptotic data are done. It is the truncation structure of the tt* equation that enables us to do those numerical studies with a satisfactory high precision.
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