Explicit Runge-Kutta Method for Evaluating Ordinary Differential Equations of type v^vi = f(u, v, v′)-Reference-Cited by-同舟云学术

Explicit Runge-Kutta Method for Evaluating Ordinary Differential Equations of type v^vi = f(u, v, v′)

Published:2024-03-22 Issue: Volume:23 Page:167-175
ISSN:2224-2880
Container-title:WSEAS TRANSACTIONS ON MATHEMATICS
language:en
Short-container-title:

Author:

Kaur Manpreet¹,Bhatti Jasdev¹,Kumar Sangeet²,Thota Srinivasarao³

Affiliation:

1. Chitkara University Institute of Engineering and Technology Chitkara University, Punjab, I1',$

2. SGTB Khalsa College, Sri Anandpur Sahib, Punjab, I1',$

3. Department of Mathematics, Amrita School of Physical Sciences Amrita Vishwa Vidyapeetham, Amaravati, Andhra Pradesh–522503, India

Abstract

The initiative of this paper is to present the Runge Kutta Type technique for the development of mathematical solutions to the problems concerning to ordinary differential equation of order six of structure v vi = f(u, v, v′ ) denoted as RKSD with initial conditions. The three and four stage Runge-Kutta methods with order conditions up to order seven (RKSD7) have been designed to evaluate global and local truncated errors for the ordinary differential equation of order six. The framework and evaluation of equations with their results are well established to obtain the effectiveness of RK method towards implicit function satisfying the required initial conditions and for obtaining zero-stability of RKSD7 in terms of their accuracy with maximum precision under minimal processing.

Publisher

World Scientific and Engineering Academy and Society (WSEAS)

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