With aid of the Wolfram Mathematica package, this study investigates the solutions of a nonlinear model with strong nonlinear- ity, namely; the Sharma-Tasso-Olver equation. We use the improved Bernoulli sub-equation function method in acquiring the analytical so- lution to this equation, we successfully obtain one-singular soliton so- lution with exponential function structure. Through the obtained ana- lytical solution, the finite forward difference method is used in approx- imating the exact and numerical solutions to this equation. We check the stability of the finite forward difference method with this equation using the Fourier-Von Neumann stability analysis. We find the L2 and L∞ norm error to the numerical approximation. We present the in- teresting 3D and 2D figures of the obtained singular soliton solution. We also plot the graphics of the numerical error, exact and numeri- cal approximations data obtained in this study by using the MATLAB package.