tunable numerical integration

T-integration, which stands for "tunable numerical integration, " is a fast, accurate, and numerically stable numerical integration formula given by X_n = X_(n - 1) + T G[P((d X)/(d t))_n + (1 - P)((d X)/(d t))_(n - 1)], where X is the integral, d X/d t is the integrand, P and G are "phase" and "gain" tuning parameters, n refers to the number of the iteration being evaluated, and T is the integration step size.