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A new Runge-Kutta method, with phase-fitted and amplification-fitted is constructed for solving first-order ordinary differential equations with periodic solutions. This new method is based on the Runge-Kutta 3/8 Rule with fourth algebraic order. In the numerical results the new method is compared with the existing method; which show that the new method is more efficient.
Numbers parts-whole relationship is mainly represented by number bonds in the Malaysian year one mathematics textbooks. Seldom tasks are given to encourage students to create their own representations. The purpose of this study was to investigate how year one students represent and solve word problems based on numbers parts-whole relationship. On this account a cross sectional survey was conducted...
An extended 2-point one-step block method formula with order four is formulated for solving stiff initial value problem. The method is similar to Runge-Kutta method which has a self-starting formula. The approximation solutions at two points will be computed simultaneously by integrating the coefficients over the closest point in the block. The accuracy and the stability properties of the method will...
In this paper, a variable step size and variable order strategy ( VSVO) used in the block method is developed for solving directly the second order two-point boundary value problems (BVPs). The variable step size and variable order strategy managed to reduce the total step and assure the accuracy of the method. The proposed block method can compute the solutions at two points simultaneously and adapted...
Credit risk theory for valuation corporate bond is usually expressed as zero coupon bond. In real bond trading, the most common form of debt is coupon bond. This paper developed model of multiperiods coupon bond with classical approach as default time rule. It means that default occurs when the firm cannot fulfill its payment obligation at coupon date and/or at the maturity date. Some assumptions...
This paper presents 4-point 1-step block method (4LBVP) to solve the linear 2nd order boundary value problem (BVP) with Dirichlet boundary condition. 4LBVP will solve the linear 2nd order BVP with Dirichlet boundary condition directly without the need to reduce it first into the system of 1st order equations. 4LBVP will produce several numerical solutions simultaneously in one step. The formulation...
This paper will implement the use of two-point block method in the form of predictor-corrector Adams-Moulton to solve first order neutral delay differential equations (NDDES) of pantograph type. This two-point block method will compute the numerical solution at two points simultaneously. This method will approximate the solutions using constant step size. The delay solutions for the unknown function...
The numerical solution of neutral delay differential equation (NDDE) with variable step size implementation in multistep block method is addressed in this paper. The strategy of variable step size was actually from the idea in adapting the step size control mechanism in the block method that allows each block to have different step size ratios as it moves in the interval. Special attention is paid...
The differential transform method is extended to solve the Cauchy type singular integral equation of the first kind. Bounded solution of the Cauchy type singular integral equation is discussed. Numerical results are shown to illustrate the efficiency and accuracy of the present solution.
This paper is concerned with a mathematical derivation of the nonlinear time-discrete Technology Emission Means (TEM) model that discuss its behavior from the perspective of discrete dynamical systems. Nonlinear time-discrete dynamics tends to chaotic behavior. The addition of a control parameter into the dynamics of this model has led to new results in the field of time-discrete control systems....
The atom-bond connectivity (ABC) index is one of the recently most investigated degree based molecular structure descriptors that have applications in chemistry. For a graph G, the ABC index is defined as equation, where du denotes the degree of a vertex u in G. In this paper, we obtain the general formula of the ABC index for certain trees and unicyclic graphs with their representing by Alkanes and...
The Objective of this research is to examine the effects of Mathematics learning utilizing the group meta cognitive approach (GMCA), learning with classical meta cognitive approach (CMCA) as experimental groups, and the conventional learning (CL) as control group among students of public Junior High School 12 and 15 in Bandung. The research method which used is an experimental method with prior knowledge...
The purpose of this study was to identify factors that influence students' performance in the Faculty of Science and Technology, Universiti Kebangsaan Malaysia (UKM). Respondents in this study consisted of 10 students with the highest Cumulative Grade Point Average (CGPA) in each school. The level of importance of each criterion was determined using the Analytic Hierarchy Process (AHP). The findings...
In this paper, we introduce the concept of fuzzy θ-semi-generalized continuous mapping by using a fuzzy θ-semi-generalized closed set that generalized the most forms and properties of fuzzy continuity. We also introduce the concept of fuzzy θ-semi-generalized closed (resp. fuzzy θ-semi-generalized open) mappings and obtained some of their characterizations. Several interesting results and counterexamples...
Let G be a simple connected molecular graph. The eccentric connectivity index ξ(G) is defined as equation, where deg(ν) denotes the degree of vertex v and ec(ν) is the largest distance between ν and any other vertex u of G. In this paper, we construct the general formulas for the eccentric connectivity index of unicyclic graphs with application to cycloalkanes.
Mathematical thinking involves mental operations that are facilitated by the learners' mathematics knowledge and their positive disposition towards mathematical problem solving. It improves problem solving process by adapting various heuristic strategies as well as monitoring and controlling their outcomes in meta-cognitive manner. Thus, it is vital to identify the mathematical thinking level of pre-university...
This paper emphasizes on the class of analytic function which is univalent in the open unit disk. The main objective of this paper is to study the two new subclasses of bi-univalent Ma-Minda starlike function involving Fox-Wright function of the function classs σ. By the generalization of Fox-Wright function, the estimates of the coefficients |a2| and |a3| for another function in these new subclasses...
This paper presents an improvement of the existing interval symmetric single-step method ISS1 which will be called the interval midpoint symmetric single-step method IMSS1. The term ‘midpoint’ is referred to the updated midpoints used in every step in the method. The idea of midpoint will potentially reduce the time and improve the effectiveness of the method. This method is tested numerically in...
The purpose of this paper is to solve directly the second order delay differential equations (DDEs) using The extended two and extended three point implicit one-step block methods using constant step size. The formulae for the extended two and extended three point implicit one-step block methods will be derived using Lagrange interpolation polynomial. The stability polynomials for the methods are...
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