Parallel Diagonally Implicit Runge-Kutta Methods For Solving Ordinary Differential Equations

This thesis focuses on the derivations of diagonally implicit Runge-Kutta (DIRK) methods with the capability to be implemented by parallel executions. A few new methods are proposed by having sparsity patterns which enable the parallelization of methods. In the first part of the thesis, a fifth order DIRK suitable for two processors parallel executions and DIRK methods of fourth and fifth orders suitable for three processors are proposed. The executions of these methods are done by using fixed stepsizes on a set of nonstiff problems. The regions of stability are presented and numerical results of the methods are compared to the existing methods. Parallel computations show significant time reduction when solving large systems of nonstiff ordinary differential equations (ODEs). The subsequent part of the thesis discusses on embedded DIRK methods suitable for two processors implementations. Two 4(3) and also two 5(4) embedded DIRK methods with adequate stability regions to solve stiff ODEs are proposed. Numerical experiments on stiff test problems are done based on variable stepsize strategy. An existing code for solving stiff ODEs suitable for embedded DIRK with equal diagonal elements is modified to accommodate the new methods with alternate diagonal elements. Comparisons on numerical results to existing methods show a competitive efficiency when solving small systems of stiff ODEs. A parallel code is developed with the same capability of the modified sequential code to handle stiff ODEs, linear and nonlinear problems. All algorithms are written in C language and the parallel code is implemented on Sun Fire V1280 distributed memory system. Three large scales of stiff ODEs are used to measure the parallel performances of the new embedded methods. Results show that speedups increased as the dimensions of the problems gets larger which is a significant contribution in reducing the cost of computations

Penyelesaian terus persamaan pembezaan biasa peringkat tiga menggunakan kaedah blok hibrid kolokasi diperbaiki

The improved block hybrid collocation method (KBHK(B)) with two off-step points and four collocation points is proposed for the direct solution of general third order ordinary differential equations. Modification is done by adding first derivative of third order function into the general form of block hybrid collocation method to yield KBHK(B). Both main and additional methods are derived via interpolation (power series function) and collocation of the basic polynomial. An improved block method is derived to provide the approximation at five points concurrently. Zero stability, consistency, convergence and absolute stability region of KBHK(B) are investigated. Some numerical examples with exact solution are tested to illustrate the efficiency of the method. KBHK(B) is compared by other block hibrid collocation method in term of global error and step number. It is shown that KBHK(B) generates minimum global error with minimum step number

Oscillation Criteria for Linear Neutral Delay Differential Equations of First Order

Some new sufficient conditions for oscillation of all solutions of the first-order linear neutral delay differential equations are obtained. Our new results improve many well-known results in the literature. Some examples are inserted to illustrate our results

Oscillation Criteria for Linear Neutral Delay Differential Equations of First Order

Some new sufficient conditions for oscillation of all solutions of the first-order linear neutral delay differential equations are obtained. Our new results improve many well-known results in the literature. Some examples are inserted to illustrate our results

Industrial Training as a Benchmark of the Employability for the Mathematical Sciences Students of UKM

AbstractIndustrial Training course (ITc) is a student's placement programme in organizations outside the Universiti Kebangsaan Malaysia (UKM). The aims of the training are to expose students to real working environment and enhance the knowledge and skills in their profession. The program is expected to produce students with competencies required by employers. This study was conducted to determine the effectiveness of the ITc in providing work experience to students of Mathematical Sciences. In addition, feedback from the industries on skills and abilities of Mathematical Sciences students in performing their tasks is obtained. Information from students and employers are collected through questionnaires which were distributed to all Mathematical Sciences students who undergo ITc and the employers during the ITc assessment visits. Analysis of the survey shows that overall, Mathematical Sciences students agreed that the program is helpful in providing exposure and experience to them. From the perspective of employers, the findings show that the employers are satisfied with the skills and abilities of the students in carrying out the assigned tasks

Teaching Science and Mathematics in English Steering Mastery in English Language Amongst Sciences Students in UKM

AbstractThis study was conducted to ascertain teaching Science and Mathematics in English will enhance English proficiency amongst the science stream students in UKM. The study found that the students agreed that the teaching of Science and Mathematics in English can improve their English proficiency. The results showed that teaching Science and Mathematics in English is capable of being a driven force in mastering basic English language and communication, and also in improving the explanation of the concept of Science and Mathematics in English

Students’ Inclination towards English Language as Medium of Instruction in the Teaching of Science and Mathematics

AbstractMalay language, the national language of Malaysia has been the medium of instruction for Science and Mathematics for the past four and a half decades in Malaysia. The government however changed the medium of instruction of these subjects to English in January 2003. The “Teaching and Learning of Science and Mathematics in English” (PPSMI) policy was implemented in all primary and secondary schools. It aims to improve the English language proficiency among students as well as the learning and achievement level in science and mathematics. This paper presents findings of the study on students’ inclination towards English language as medium of instruction in teaching and learning of Science and Mathematics in Higher Learning Institutions in Malaysia. The respondents were 291 undergraduate students from the Faculty of Science and Technology (FST) and Faculty of Education (FPEND) of Universiti Kebangsaan Malaysia (UKM). A questionnaire pertaining to students’ inclination was used as research instrument. Using descriptive statistics, ANOVA and t-test, the study found that undergraduate students of FST and FPEND had an inclination towards English as medium of instruction in the teaching and learning of Science and Mathematics. Using the Post-Hoc test, it is found that Indian students and students from other races than Malay and Chinese have greater inclination towards English as medium of instruction in teaching and learning of Science and Mathematics in UKM for both faculties. However, FST students who studied in Mandarin and Tamil at pre-university level (STPM) had higher inclination compared to those who used Malay language or even English

Pemilihan pengajar berkesan menggunakan kaedah proses hierarki analisis kabur

This study is carried out to explore the method of selecting a lecturer with the most effective teaching skill. The method that has been identified is Fuzzy Analytical Hierarchy Process (AHP). The selection by students using this method is more reliable compared to the existing one, which uses the average score given by students. This is because Fuzzy AHP takes into account the relative comparison between lecturers as well as includes the degree of importance given by students in each of the factors that contribute to effective teaching. Fuzzy numbers are used in the pair wise comparison in order to alleviate the problem of inflexibility in the process of choosing the lecturer with the most effective teaching skil

Variational Iteration Method and Sumudu Transform for Solving Delay Differential Equation

In this research, a new approach is presented for solving delay differential equations (DDEs) which is a blend of Sumudu transform and variational iteration method (VIM). A general Lagrange multiplier is used to construct a correction functional. This is done with an uncommon Sumudu transform alongside variational theory. A few numerical cases were solved to demonstrate methodology of this new approach. Objective of this research is to reduce the complexity of computational work compared to the conventional approaches. It can be concluded that the amount of evaluation is reduced but at the same time the results are comparable as in the previous works