Cube Arithmetic: Improving Euler Method  for Ordinary Differential Equation using Cube Mean

Samsudin, Nooraida; Yusop, Nurhafizah Moziyana Mohd; Fahmy, Syahrul; Mokhtar, Abdul Halim

doi:10.11591/ijeecs.v11.i3.pp1109-1113

Cited by 8 publications

(6 citation statements)

References 5 publications

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“…There are three sets of RL circuit equations with a different value for voltage (V), resistor (R) and inductor (L). The equation to solve the speed of RL circuit equation [44] come out with (5). Table 2 shows the results of the time needed for each device to complete the simulation in three schemes (polygon, harmonic-polygon, and centroidal-polygon).…”

Section: Resultsmentioning

confidence: 99%

“…Euler method produces simple numerical solutions and enforces low computational cost to solve the ordinary differential equation (ODE) for a given initial value problem (IVP) [1]- [9]. Although the Euler method gives a simple solution, this method lacks accuracy [5], [9]. The Euler method will contribute to an error at every step size implied in the solution [8].…”

Section: Introductionmentioning

confidence: 99%

“…The problem in solving the RL circuit equation is the speed of each scheme takes to complete the simulation. As discussed in the first paragraph, the Euler method can solve the small step size but lacks computational cost [5]. This research will analyze comparing new modified Euler method centroidal polygon (CP) to polygon (P) and harmonic polygon (HP) [22].…”

Section: Introductionmentioning

confidence: 99%

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Centroidal-polygon: a new modified Euler to improve speed of resistor-inductor circuit equation

Zulkifli

Samsudin

et al. 2021

IJEECS

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Two types of first-order circuits are resistor-capacitor (RC) and resistorinductor (RL). This paper focuses on the RL circuit equation. The centroidalpolygon (CP) scheme will be tested using SCILAB 6.0 software. This new scheme (CP scheme) is addressed to improve the speed. For the first order circuit equation, the complexity is focused on the time complexity, which is speed of the time taken to complete the simulation in the electrical part. The CP scheme is compared with the previous studies, polygon (P) and harmonic-polygon (HP). The result shows that the CP scheme is less computational and an alternative to solve the first order circuit equation, and get the result quickly compared with the previous research.

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Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Centroidal-polygon: a new modified Euler to improve speed of resistor-inductor circuit equation

Zulkifli

Samsudin

et al. 2021

IJEECS

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“…The midpoint method is more stable than Heun's method [3]. The midpoint method is also credited with having a simpler implementation and being the most sensible method to improve the Euler method [5] since it uses an approximation of the gradients at a midpoint of the prediction interval. ZulZamri developed the Euler method using the midpoint method by combining the Euler method equation and a mean concept.…”

Section: Literature Reviewmentioning

confidence: 99%

Improving Euler Method using Centroidal-Polygon Scheme for Better Accuracy in Resistor-Capacitor Circuit Equation

Zulkifli

Samsudin

Yusof

2022

J. Phys.: Conf. Ser.

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A first-order ordinary differential equation (ODE) is a function with two variables defined in the xy-axis of a field. Various numerical methods, such as the Euler method, Runge-Kutta method, Heun’s method and others, are used to solve ODEs, with varying computational costs and accuracy. The Euler method can only solve the first derivative equation with the simplest implementation at the lowest cost of computation, but it produces less accurate results. This research focuses on improving the Euler method to increase its accuracy. A new scheme called Centroidal-Polygon (CP) is used in this study. The CP scheme is tested on the Resistor-Capacitor (RC) circuit equation to ensure that it can be used in fields other than mathematics and computation. The RC circuit equation is used to compute maximum error and assess the accuracy of the CP scheme and its counterparts. The circuit equation’s accuracy in the RC circuit equation is determined by the time constant (τ). This research used Scilab 6.0 software to analyze the maximum error. The performance of the CP scheme was compared to the Polygon, Harmonic-Polygon, and Cube-Polygon schemes, which are all enhanced Euler methods. The results show that the CP scheme achieves higher accuracy while requiring less computing time. In future studies, the CP scheme will be applied to the RCL circuit equation and second-order ODE to ensure the CP scheme can be used in all applications.

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“…B. M. Hame et al [5] discussed the accuracy of Euler and modified Euler technique. Detailed explanation and higher-level applications can be found in [6]- [10] [11] .In this research, Modified Euler method has been applied to solve the IVPs of ODEs. Here, Different step sizes have been used for finding the best approximation.…”

Section: Introductionmentioning

confidence: 99%

Accuracy Analysis for the Solution of Initial Value Problem of ODEs Using Modified Euler Method

Arefin¹,

Islam²,

Gain³

et al. 2021

IJMSC

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There exist numerous numerical methods for solving the initial value problems of ordinary differential equations. The accuracy level and computational time are not the same for all of these methods. In this article, the Modified Euler method has been discussed for solving and finding the accurate solution of Ordinary Differential Equations using different step sizes. Approximate Results obtained by different step sizes are shown using the result analysis table. Some problems are solved by the proposed method then approximated results are shown graphically compare to the exact solution for a better understanding of the accuracy level of this method. Errors are estimated for each step and are represented graphically using Matlab Programming Language and MS Excel, which reveals that so much small step size gives better accuracy with less computational error. It is observed that this method is suitable for obtaining the accurate solution of ODEs when the taken step sizes are too much small.

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Cube Arithmetic: Improving Euler Method for Ordinary Differential Equation using Cube Mean

Cited by 8 publications

References 5 publications

Centroidal-polygon: a new modified Euler to improve speed of resistor-inductor circuit equation

Centroidal-polygon: a new modified Euler to improve speed of resistor-inductor circuit equation

Improving Euler Method using Centroidal-Polygon Scheme for Better Accuracy in Resistor-Capacitor Circuit Equation

Accuracy Analysis for the Solution of Initial Value Problem of ODEs Using Modified Euler Method

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