This paper discusses the numerical approach used to solve the parabolic partial differential equation. The Schmidt method and the Crank-Nicolson method are covered in this paper. These numerical methods are employed to discover a partial differential equation’s approximate solution. These methods are unquestionably effective and practically good for solving partial differential equations, and they are all used to assess the degree of accuracy of each method. The Crank Nicolson method is exposed to both analysis of stability and analysis of absolute error in order to help mathematicians and engineers to understand how well these numerical solutions actually perform approaches. With Boundary condition \(P(0,t) = P(L,t) = 0\) and \(P(x,0) = f(x), 0 < x < L\) , the heat equation \( \frac{\partial P}{\partial t} = c^2 \frac{\partial ^2 P}{\partial x^2} \) Where c is constant, x is space variable, L is the length of the rod, t is the time variable, and P(x, t) is the temperature function with time t, and position x. The above heat equation is analysed using method of variable separation. The findings are then compared to the analytical solution after the identical equation is solved using both the Schmidt and Crank Nicolson techniques. We create a comparison table of the approximate and exact solutions in order to get and assess the level of accuracy of the numerical findings. We note that the exact and approximative solutions agree well, and we compare the computational effort required by the various proposed solutions. Now we identify the error in the suggested techniques that accounts for the proposed method’s superiority. According to the result of the study, the Crank Nicolson approach is ultimately more efficient than the Schmidt approach and also yields less error.