A wide variety of scientific and engineering domains make use of partial integro-differential equations. Several
numerical methods for solving a partial integro-differential equation with a weakly sin-gular kernel are presented in
this work. A partial integro-differential equation with an initial condition and specified boundary conditions may be
solved using these approaches. Based on finite-difference methods and the product trapezoidal numerical
integration rule, we design many computational algorithms. The modeling of physical processes incorporating
viscoelasticity forces presents this challenge. The implicit approach of Crandall, the Crank-Nicolson formula, the
forward-Euler explicit scheme, the backward-Euler implicit technique, and the finite-difference methods established
are all based on these frameworks. In terms of the space variable, three of the approaches exhibit accuracy at the
second order. To a greater extent than the alternatives, Crandall's plan is accurate. To ensure the consistency and
precision of the methods described, the numerical solutions to a test issue are provided.