ANALYTICAL SOLUTION OF THE RELATIVISTIC KLEIN-GORDON WAVE EQUATION

In this study, the solution to Klein-Gordon equations with focus on analytical methods is discussed. The analytical methods used in this research are the Variational Iteration Method (VIM) developed by Ji-Huan He, Adomian Decomposition Method (ADM) by Adomian and New Iterative Method (NIM) developed by Daftardar Gejji and Jafari. The modified Adomian Decomposition method by Wazwaz was used to solve the linear inhomogeneous and nonlinear Klein-Gordon equations to accelerate the convergence of the solution and minimizes the size of calculation while still maintaining high accuracy of the analytical solution. All the problems considered yield the exact solutions with few iterations. The solutions obtained were compared with the exact solution and the solutions obtained by other existing methods. The solutions obtained by the three methods yield the same results and all the problems considered show that the Variational Iteration Method, Adomian Decomposition Method and New Iterative Method are very powerful and potent in solving Klein-Gordon equations and can be used to obtain closed form solutions of linear and nonlinear differential equations (ordinary and partial)

Malaysian PBL Approaches: Shaping World-Class TVET Skills towards IR 4.0

An Industrial Revolution 4.0 promoted by Malaysian government entitles the rapid growth of manufacturing sector thus promotes a multi-level of workforce and skilled work force needed to satisfy the rapid technological development application. The challenges arise on preparing the individuals to meet with the current business at adequate skills level and the student need to be prepared in such way satisfied the business expectations. Looking into this situation, this paper aims to study the concept of correlation between active learning method known as Problem-Based Learning (PBL) Method and required employability skills in TVET. As an initiative to enrich the future opportunity on empowering TVET skills, this study assumes that there is positive relationship between employability skills and PBL approaches in improving student’s quality and skills. The method of study involves documentation analysis on previous research to proves the importance of employability skills in enhancing student’s competencies and the effectiveness of Problem-Based Learning Method in preparing the students to meet the expectations. The main findings of this study claimed that there was a positive relationship between employability skills and PBL learning method. Result acknowledge that PBL has the ingredients to help develop employability skills and student’s behavior. Through PBL, students learn to become more associates in the teaching and learning processes as they take responsibility throughout the learning process. It would suggest that the educational institution should emphasize the needs of the industry and students by creating awareness and guiding the students in self-analysis and in acquisition of skills