Nonlinear equations arise in many fields of science and engineering. Solving these equations numerically is often challenging due to their complex nature. Finding roots of nonlinear equations is challenging in numerical analysis. Analytical solutions to nonlinear equations are often intractable necessitating the use of numerical methods. In this paper, we proposed a newly iterative technique for simulation of nonlinear equations based on trapezoidal rule of integration. Theoretical analysis and numerical experiments demonstrate and effectiveness of newly proposed iterative technique for solving a wide range of nonlinear problems. When working with certain higher order functions, the suggested approach greatly improves the trapezoidal rule and gets outcomes the error value problem, even when solving for a single interval. This provides grounds for confidence in the proposed method and provides the prospect for further refinement in future work.