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In this study, the numerical comparison is performed in solving first-order neutrosophic initial value problems employing two algorithms, namely, the Euler and fourth-order Runge-Kutta (RK4) methods in the neutrosophic environment. As an example of such kind of problem, the model y^' (t)=0.5∙y(t) on [0,2] is chosen, but in the case of the additional neutrosophic initial condition y(0)=⟨(0.8,1.0,1.3)⟩. This problem is represented as crisp-endpoint systems by means of ( α,β,γ )-cut approach, and then, it is solved numerically at each cut level while using exact solution as a reference. In accordance with the iteration results, the maximum absolute error of the Euler algorithm at h=0.2 is 1.619×10^(-1) at point t=2, whereas for the RK4 approach, this value is 2.7×10^(-6), meaning that the improvement degree reaches about five orders of magnitude. The analysis of step refinement confirms the convergence orders of the methods that are 1.00 and 4.00 for the Euler and RK4 approaches, respectively.