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.
The Euler method is one of the oldest methods to solve differential equation problems. The Euler method produces the simplest solution. However, although is not computationally expensive, the Eulermethod is lack of accuracy. To improve the Euler method, the researcher proposed a new scheme for better accuracy. The Euler method equation and the mean method were combined to enhance this method. As the improvement basis, the researcher used the Centroidal mean and the midpoint method or Polygon to improve the Euler method. The combination of the Euler and Centroidal mean is known as Centroidal Polygon (CP) scheme. The CP scheme was used to solve first-order non-linear Ordinary Differential Equations (ODE). The researcher used SCILAB 6.0 software to solve the equation and the CP scheme was tested in three different step sizes (0.1,0.01, and 0.001). Aside from that, the researcher had compared the CP scheme with previous schemes such as ZulZamri's Polygon (P) scheme, Nurhafizah's Harmoni-Polygon (HP) scheme, and Nooraida's Cube-Polygon (CuP) scheme to ensure that the CP scheme is more accurate than previous research. When the maximum error is calculated by subtracting the scheme and exact solution, the results show that the CP scheme delivers the highest accuracy results in the shortest amount of time. The new enhanced, modified Euler method is useful for other researchers to achieve good accuracy at low computational cost as an alternative to the more computationally expensive methods.
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.
Compliance rate towards consumption of oral nutritional supplement (ONS) is low among geriatric patients. Thus, this study aimed to examine factors affecting low compliance of ONS intake among a sample of geriatric patients. A crosssectional survey was carried out involving 30 geriatric patients being prescribed with ONS during their stay in Hospital Kuala Lumpur. Information on compliance rate and influencing factors were collected through interview and observation. Nutritional status was assessed using anthropometry and Patient Generated Subjective Global Assessment (PG-SGA). 50.0% subjects were underweight and 70.0% and 30.0% were moderate and severely malnourished, respectively. A total of 43.3% were categorised as low, 53.4% medium and 3.3% high compliance towards consumption of ONS. Most of the subjects with low compliance agreed expressed that they need more nursing support (53.8%). Less than half perceived they had been given the needed nursing support (44.4%), and with respect to ONS: knowledgeable (38.5%), timely given (37.5%), understood the importance (35.7%), were able to finish it (35.0%), well-aware of the reasons of prescription (33.3%), satisfied with its taste (33.3%), received suitable volume (33.3%), satisfied with the texture (31.6%), and received suitable frequency (28.6%). In conclusion, approximately 40% of subjects had low compliance towards ONS. Awareness and nursing support were important factors associated with low compliance. There is a need to ensure adequate nursing support and education been given to patients prescribed with ONS in order to increase the compliance rate.
Numerical method is a technique of obtaining the nearest approximation for the solution of various problems that can be described in the form of derivative equations. Engineering issues cannot be simply overcome using analytical concepts. This study aims to propose a new scheme from an enhanced Euler method for testing the resistor-inductor (RL) circuit equation. For this purpose, the paper proposes the Euler Root Mean Square (ERMS), a modified Euler method with improved accuracy. It will justify that the new scheme can be as accurate as possible in providing the exact solution by applying an average concept of using root mean square. It will focus on this accuracy by comparing the exact solution and actual solution between the new ERMS scheme and a modified Euler known as Euler Arithmetic. This study has demonstrated that the ERMS provided solutions that are similar to the exact solutions at t=0.5. It proves that an enhanced Euler method can be applied in various fields, especially in electrical engineering. In conclusion, the ERMS can be used as an alternative algorithm to solve RL circuit problems.
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