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Let $\mathbb{Z}_p[x]$ be the set of all functions whose coefficients are inthe field of $p$-adic integers $\mathbb{Z}_p$. This work considers a problem offinding a root of a polynomial equation $P(x)=0$ where$P(x)\in\mathbb{Z}_p[x]$. The solution is approached through an analogue ofOlver's method for finding roots of polynomial equations $P(x)=0$ in$\mathbb{Z}_p$.

Olver's Method for Approximating Roots of p-Adic Polynomials Equations