Centroidal Polygon: A New Enhancement of Euler to Improve Accuracy of First Order Non-Linear Ordinary Differential Equation

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 Euler method 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

Centroidal Polygon: A New Enhancement of Euler to Improve Accuracy of First Order Non-Linear Ordinary Differential Equation

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 Euler method 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

Establishment of family court in Malaysia: Learning from Singapore and Australia / Idzaa Nurul Amiraa Alias … [et al.]

The main aim of this study is to propose for the establishment of civil family court with exclusive jurisdiction over family matter under one roof that could function as one stop center for family dispute in every state. In order to do this, we shall examine the family court system in two different countries, which adapt different legal system of family court and comprise various features and characteristics of the courts. It should be note that in Malaysia, there is no single family court with exclusive jurisdiction in dealing with family matters. Malaysia family court systems are divided into two, one is for Muslims and the other for non- Muslims. For Muslim, their cases will be heard before the Shariah Court. While for non-Muslim, their cases will be heard before various level of court which has their own jurisdiction. As a result, it required applicant to file the application in different court. With the establishment of family court, it would put an end to the above said problem. In order to achieve the aim and objective of this research, the main questions that we hope to answer in this research, firstly on how does the current regime governing civil family dispute in Malaysia and the problems exist in Malaysia. Secondly, the research question is what the features adapted in family court at Singapore and Australia. Thirdly, on how does other countries successfully operate their family court system. It will also briefly discuss the implementation of family court system in Australia and Singapore that have been chosen as model countries since they have a well- developed family court. Both countries had successfully established family court as part of the court system. We need to examine other's country family court and choose the best features, facilities and services in order to establish family court in Malaysia