Use of a sine cosine algorithm combined with Simpson method for numerical integration

The sine cosine algorithm (SCA) is one of the most recent nature-inspired meta-heuristic optimisation algorithm, which the mathematical model based on sine and cosine functions. SCA has validated excellent performance in solving continuous problems and engineering optimisation problems. In this paper, we propose a new algorithm that encompasses the features of sine cosine algorithm and Simpson method (SCA-SM). The proposed procedure consists of two phases: in the first phase, the of sine cosine algorithm are used to find the optimal segmentation points on the integral interval of an integrand. In the second phase, the approximate integral value of the integrand is then calculated by a Simpson method. Numerical simulation results show that the algorithm offers an effective way to calculate numerical value of definite integrals, and it has a high convergence rate, high accuracy and robustness.