A new Euler scheme based on harmonic-polygon approach for solving first order ordinary differential equation

Yusop, Nurhafizah Moziyana Mohd; Hasan, Mohammad Khatim; Wook, Muslihah; Amran, Mohd Fahmi Mohamad; Ahmad, Siti Rohaidah

doi:10.1063/1.5005435

Cited by 7 publications

(11 citation statements)

References 1 publication

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“…This scheme specifically describes the aspect and transfers the schemes into the software code. Most implementations have resolved the basic software code designed to explain how it is implemented [8]. The approach for developing mathematical software is as follows:…”

Section: Resultsmentioning

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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Section: Resultsmentioning

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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“…Before using the mathematical software, algorithm development must be done first. Algorithm refers as instructions for solving pro blem using simple language [10][11]. According to [12], construction process in mathematical software includes as follows.…”

Section: Methodsmentioning

confidence: 99%

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

Samsudin¹,

Yusop²,

Fahmy³

et al. 2018

IJEECS

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The Euler method is a first-order numerical procedure for solving Ordinary Differential Equation (ODEs) problems. It is an effective and easy method to solve initial value problems. Although Euler provides simple procedure for solving ODEs, there have been issues such as complexity, time of processing and accuracy that compelled the use of other, more complex, methods. Improvements to the Euler method have attracted much attention resulting in numerous modified Euler methods. This paper proposes Cube Arithmetic, a modified Euler method with improved accuracy. The efficiency of Cube Arithmetic was compared with Euler Arithmetic and tested using SCILAB against exact solutions. Results indicate that not only Cube Arithmetic provided solutions that are similar to exact solutions at small step size, but also at higher step size, hence producing more accurate results.

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“…H is the upper and lower quartile [22]. Trimean have been used to estimate wavelet coefficient [23] while [21] apply trimean in colour model constancy and [25] combine Trimean and Quartile to estimate the variance.…”

Section: H Andmentioning

confidence: 99%

Semi Non-Standard Trimean Algorithm for Rosenzweig-MacArthur Interaction Model

Hasan¹,

Othman²,

Karim³

et al. 2018

Int. J. Adv. Sci. Eng. Inf. Technol.

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Most real world natural systems are shows seasonal behaviour due to seasonal environmental or climate change. As a results, many species display seasonal changes in their life history parameters. It is crucial to comprehend how the seasonal forcing controls the behaviour of the population dynamics. The Rosenzweig-MacArthur model is a system with at least two ordinary differential equations used in population dynamics to model the interaction of predator and prey bonding. Rosenzweig-MacArthur model overcome the weakness of Lotka-Volterra model to simulate interaction between two species. In Rosenzweig-MacArthur model, logistic growth rate of prey is resource limited. The model utilizes Holling type II as the functional response representation. The purpose of the study is to construct method to improve simulation on the behaviour of interactions between species and predicting equilibrium point accurately and fast. Current methods seem to predict accurately the equilibrium point if only small mesh size used. Using small mesh size will require long simulation time to predict the equilibrium point. Able to increase the mesh size will increase the speed of predicting the equilibrium point. In this paper, we propose three new semi non-standard trimean algorithms to simulate the behaviour of interaction between species represented by Rosenzweig-MacArthur model. The new algorithms apply a hybrid of semi non-standard approach and trimean to approximate the nonlinear terms in the differential equation model. Two cases of experiment conducted to examine the performance of all three semi non-standard schemes. Result shows that all three new semi non-standards schemes accurately predict the equilibrium point (0.25, 0.46875) even using big mesh size (6. 4 = h and 1. 2 = h) for both cases. Thus, all three semi non-standard schemes fulfil the purpose of this study.

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A new Euler scheme based on harmonic-polygon approach for solving first order ordinary differential equation

Cited by 7 publications

References 1 publication

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

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

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

Semi Non-Standard Trimean Algorithm for Rosenzweig-MacArthur Interaction Model

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