We study the conformal scattering of massless scalar waves in Minkowski spacetime. The conformal scattering problem is formulated as a Goursat (characteristic initial value) problem of the physical wave equation in compactified double-null coordinates, including the neighborhood of spatial infinity $i^0$. As null infinities ${\mathcal{I}}^{\pm }$ lie on the domain boundary by construction, asymptotic radiation is directly accessible. We consider three physical scenarios: free wave propagation, scattering off a Pöschl-Teller (PT) potential, and the semilinear $|\varphi {|}^{n-1}\varphi$ wave equation. For multipole numbers $\ell =0$, 1, an explicit stencil, averaging along the spatial direction, yields globally second-order convergent results. For $\ell \ge 2$, an implicit stencil averaging along the temporal direction is required for numerical stability. Although the singular $i^0$ reduces the convergence of the radiation data on ${\mathcal{I}}^{+}$ to first order, Richardson extrapolation enhances the effective convergence rate to approximately 1.5. For PT scattering, our method accurately computes scattering quantities, notably the phase shifts induced by the potential. In the semilinear case, our method captures the physical signatures of a self-defocusing Kerr nonlinearity, including self-phase modulation and spectral broadening. The compactified double-null framework proves to be simple and efficient, suggesting a promising approach to the global evolution of conformal scattering.

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• Wave scattering
• Numerical relativity