Formulative Visualization of Numerical Methods for Solving Non-Linear Ordinary Differential Equations

Authors

  • Jeevan Kafle Central Department of Mathematics, Tribhuvan University
  • Bhogendra Kumar Thakur Central Department of Mathematics, Tribhuvan University
  • Grishma Acharya Central Department of Mathematics, Tribhuvan University

DOI:

https://doi.org/10.3126/njmathsci.v2i2.40126

Keywords:

Ordinary Differential Equations, Numerical Methods, Error Function and Error Analysis., 2020 Mathematics Subject Classification: 65L06, 65L10

Abstract

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.

Downloads

Download data is not yet available.
Abstract
305
PDF
241

Downloads

Published

2021-10-09

How to Cite

Kafle, J., Thakur, B. K. ., & Acharya, . G. . (2021). Formulative Visualization of Numerical Methods for Solving Non-Linear Ordinary Differential Equations. Nepal Journal of Mathematical Sciences, 2(2), 79–88. https://doi.org/10.3126/njmathsci.v2i2.40126

Issue

Section

Articles