Numerical simulation of nonlinear equations by converting quadrature rule to iterative technique

In computational mathematics, numerical integration is an essential method that yields effective approximations of definite integrals. The trapezoidal technique is one of the most popular numerical integration techniques because of its ease of use and efficiency. Unfortunately, when working with complicated functions or intervals that exhibit erratic behavior, its applicability is restricted. The goal of this research study is to examine the effectiveness and practical implications of converting the trapezoidal rule to iterative procedures through the use of fundamental theorem of calculus for numerical integration. In addition, we provide case studies and numerical experiments to show the usefulness and efficiency of the proposed iterative techniques in comparison with the conventional Trapezoidal Rule. These experiments demonstrate situations in which iterative approaches perform better than the conventional method, indicating the potential of these approaches in practical integration problems. The research findings provide insights into the transformation of simple methods such as the Trapezoidal Rule into advanced iterative approaches, hence contributing to the improvement of numerical integration methods. This study provides more dependable numerical solutions in a variety of scientific and engineering applications by increasing the accuracy and efficiency of integration techniques.