This paper presents a numerical analysis of high-order iterative methods applied to simplified turbulence models, specifically the viscous Burgers equation, a model widely used to study nonlinear phenomena in fluid dynamics. The equation is discretized in time using the Crank-Nicolson scheme, resulting in nonlinear systems that are solved using various iterative methods, including Newton, NG (based on the golden ratio), Newton-Jarratt, and the NJN method, which the authors proposed in a previous scientific article. The latter combines Jarratt’s composition with a frozen Jacobian, achieving fifth-order convergence with low computational cost. All methods were implemented in MATLAB and evaluated under different configurations of viscosity and temporal resolution. Based on the solutions obtained, an accurate and robust spatiotemporal dataset was constructed, making it ideal for training deep neural networks. This approach lays the groundwork for developing hybrid models that integrate advanced numerical techniques with machine learning algorithms, enabling new strategies for the efficient prediction and simulation of nonlinear systems of equations.