Stigating Newton's Interpolation and Lagrange Method Compared to Runge Kutt A Method in Solving First Order Differential Equations.
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Date
2022
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Kabale University
Abstract
This study investigated Newton's Interpolation and Lagrange method as compared to Runge Kuta's method in solving First Order Differential Equations. It follows research questions that include quicker and faster methods of solving first-order differential equations using Newton's interpolation and Lagrange and method of solving first-order equations using Runge-Kutta with increased accuracy comparing Newton's interpolation, and Lagrange. Study results indicate that for instance for y(0.01) in example l a combination of Newton's interpolation and Lagrange gives an absolute error of 0. 00009901. Runge Kutta's second order gives an absolute error of 0.00989951. For y(0.01) a combination of Newton's interpolation and Lagrange gives an absolute error of 0. 000084 as compared to 0. 024613585 absolute error obtained by Runge Kutta second order and the study recommends that the Numerical method used (Runge Kutta) is cumbersome and has a bigger percentage error. I therefore recommend the use of combined Newton's interpolation and Lagrange method to solve . Therefore the combination of Newton's interpolation and Lagrange gives a high accuracy as compared to Runge Kutta's second order. A combination of Newton's interpolation and Lagrange is a simpler method to use since it has less iteration as compared to Runge Kutta's second order.
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Keywords
Stigating Newton's Interpolation, Lagrange Method, Runge Kutt A Method, Solving, First Order, Differential Equations
Citation
Gumisirlza, Catheline (2022). Stigating Newton's Interpolation and Lagrange Method Compared to Runge Kutt A Method in Solving First Order Differential Equations. Kabale: Kabale University.