Simpson Double Integral Numerical Algorithm

The Simpson double integral numerical algorithm is a widely-used numerical integration method for approximating the integral of bivariate functions. Its fundamental principle involves partitioning the integration domain into multiple subintervals and applying Simpson's rule to compute the integral over each subinterval. This implementation features extensively detailed comments that guide readers through the algorithm's computational workflow and implementation details. The code demonstrates key aspects such as nested loop structures for handling two-dimensional integration domains, weight coefficient calculations for Simpson's parabolic approximations, and error control mechanisms through adaptive interval partitioning. The algorithm efficiently handles double integrals by first integrating over one variable while treating the other as constant, then integrating the result over the second variable, with clear documentation explaining the step-by-step numerical integration process.