Open AccessFormulative Visualization of Numerical Methods for Solving Non-Linear Ordinary Differential Equations
Author(s) -
Jeevan Kafle,
Bhogendra Kumar Thakur,
G. N. Acharya
Publication year - 2021
Publication title -
nepal journal of mathematical sciences
Language(s) - English
Resource type - Journals
eISSN - 2738-9928
pISSN - 2738-9812
DOI - 10.3126/njmathsci.v2i2.40126
Subject(s) - runge–kutta methods , ode , euler method , ordinary differential equation , numerical methods for ordinary differential equations , mathematics , euler's formula , l stability , explicit and implicit methods , visualization , backward euler method , linear multistep method , numerical analysis , midpoint method , differential equation , computer science , euler equations , mathematical analysis , differential algebraic equation , artificial intelligence
Many physical problems in the real world are frequently modeled by ordinary dierential equations (ODEs). Real-life problems are usually non-linear, numerical methods are therefore needed to approximate their solution. We consider dierent 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 fth-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.