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It is well known that confinings and asymptotic freedom are properties ofquantum chromo-dynamics (QCD). But hints of these features can also be observedat purely classic levels. For this purpose we need to find solutions to thecolorly-sourceful Yang-Mills equations with both confining and asymptoticfreedom features. We provide such a solution in this paper which at thenear-source region is of serial form, while at the far-away region isapproximately expressed through simple elementary functions. From the solution,we derive out a classically non-perturbative beta function describing therunning of effective coupling constant, which is linear in the couplings bothin the infrared and ultraviolet region.

A Semi-analytical Solution to Classic Yang-Mills Equations with Both Asymptotical Freedom and Confining Features