Formulative Visualization of Numerical Methods for Solving Non-Linear Ordinary Differential Equations - Kafle, Jeevan; Thakur, Bhogendra Kumar; Acharya, Grishma (Nepal Journal of Mathematical Sciences, 2021)
Many physical problems in the real world are frequently modeled by ordinary diﬀerential equations (ODEs). Real-life problems are usually non-linear, numerical methods are therefore needed to approximate their solution. We consider diﬀerent numerical methods viz., Explicit (Forward) and Implicit (Backward) Euler method, Classical second-order Runge-Kutta (RK2) method (Heun’s method or Improved Euler method), Third-order Runge-Kutta (RK3) method, Fourth-order Runge-Kutta (RK4) method, and Butcher ﬁfth-order Runge-Kutta (BRK5) method which are popular classical iteration methods of approximating solutions of ODEs. Moreover, an intuitive explanation of those methods is also be presented, comparing among them and also with exact solutions with necessary visualizations. Finally, we analyze the error and accuracy of these methods with the help of suitable mathematical programming software.