By an Extended Iteration Method to Adequate Solutions of Jerk Oscillator Containing Displacement Times Velocity Time's Acceleration and Velocity (Global Journal of Science Frontier Research, 2023)
Mathematics has applications in every aspect of real life. So many such type of real-life problems are modeled by differential equations. Therefore, differential equations are used as tools to solve many complex situations. With the help of differential equations, we can find the formula to solve many significant issues in many areas of the Anatomy and Physiology of the human body like physical, mental physical, and medical principles. Differential equations can be linear, nonlinear, autonomous, or non-autonomous. Practically, most of the differential equations involving physical phenomena are nonlinear. Hence nonlinear differential equations play a vital role in case of science and engineering. Nonlinear systems are differently classified, and the 'nonlinear jerk oscillator' is one of the most essential parts of a nonlinear system. Different types of nonlinear jerk oscillators will be analyzed using Extended Iteration Method, and the outcome may leave an impact to be better than the current results.
Keywords: jerk equation; truncated fourier series; newton’s method; angular frequency; extended iteration technique