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Published by Universitas Syiah Kuala
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Core Subject : Education,
Mathematics
2nd conference of ICMSA was held in 2006 at Penang, Malaysia.
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Articles 49 Documents
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NEWTON POLYHEDRA AND ESTIMATION TO EXPONENTIAL SUMS Atan, Kamel Arifin Mohd
Journal of ICMSA Vol 1, No 1 (2006): Pure Maths : ICMSA 2006
Publisher : Journal of ICMSA

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Abstract

The classical Newton polygon is a device for computing the fractional power series expansions of algebraic functions. Newton gave a number of examples of this process in his ”Method of Fluxions” which amount to a general method. However, it was not till much later that Puiseux proved that every branch of a plane algebraic curve defined by a polynomial equation f(x, y) = 0 has an expansionin a neighbourhood of a point (x0, y0) on the curve. In practice, the integers a, b and q can be read off from the Newton polygon and the coefficients cj can be determined successively with ever-increasing labour.
THE RELIABILITY AND CONSTRUCT VALIDITY OF SCORES ON THE ATTITUDES TOWARD PROBLEM SOLVING SCALE Sabri Ahmad et al.
Proceedings of ICMSA Vol 1, No 1 (2005): ICMSA 2005
Publisher : Proceedings of ICMSA

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Abstract

The Attitudes Toward Problem Solving Scale (ATPSS) has received limitedattention concerning its reliability and validity with a Malaysian secondaryeducation population. Developed by Charles, Lester O'Daffer (1987), theinstruments assessed attitudes toward problem solving in areas of Willingness to Engage in Problem Solving Activities, Perseverance During the Problem Solving Process and Self Confidence With Respect to Problem Solving. This study addressed the lack of information about this measure by examining the scale's reliability and its factorial structure. Subjects were 233 secondary schoolstudents. Reliability coefficients of the three subscales and the total score werehigh, indicating that the scale is stable and reliable in measuring AttitudesToward Problem Solving. Results from factor analyses imply that the ATPSSmeasures more various traits in Malaysian culture.Key words: Attitudes toward problem solving, reliability, validity
NUMERICAL SIMULATIONS OF INDIAN OCEAN TSUNAMI BY TUNA-M2 Cham Kah Loon
Proceedings of ICMSA Vol 2, No 1 (2006): Applied Mathematics
Publisher : Proceedings of ICMSA

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Abstract

The Sumatra-Andaman earthquake of magnitude 9.3 on the Richter scale occurred on 26 December 2004. It triggered off a series of tsunami waves that caused tremendous damage to the properties and lives along the affected coastal areas. The earthquake was located where the India Plate dives under the Burma Plate, and was extremely large in geographical extent, beginning off the coast of Aceh and proceeding northwesterly over a period of about 100 seconds. An estimated fault length is about 800 km, with a fault width of about 85 km and an initial vertical displacement of 11 m. There were no tsunami warning systems in the Indian Ocean to detect tsunamis, nor to warn the general populace living around the ocean. Thus, there is a need for early warning systems to predict the characteristics of tsunami propagation, including tsunami wave heights and arrival times. There are three phases of tsunami evolution, which are generation, propagation and runup. Tsunami is generated by the disturbance associated with seismic activity, explosive volcanism, and submarine landslide phenomena. Propagation of tsunami waves transports seismic energy away from the earthquake source. During the deep ocean propagation stage, the wave height is small compared to the wavelength and the ocean depth. Therefore, the linear wave theory can be applied. Tsunami runup is the most destructive phase of tsunami evolution. The wave behavior at the shoreline depends on such characteristics as the relationships between wavelength and water depth and between the wavelength of the wave and its height. This paper will present the simulations of these tsunami propagations in the Indian Ocean and discuss wave height characteristics near the coast of Sri Lanka, Bangladesh and India to highlight tsunami hazards and coastal vulnerability. The need for an early warning system in the Indian Ocean would appear urgent. The simulation is performed by means of an in-house tsunami numerical simulation model TUNA-M2 that solves the shallow water equation by the staggered finite difference method.
EFFECT OF TIME DELAY ON THE TRANSMISSION OF DENGUE FEVER I-Ming Tang
Proceedings of ICMSA Vol 2, No 1 (2006): Applied Mathematics
Publisher : Proceedings of ICMSA

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Abstract

The effect of a time delay on the transmission on dengue fever is studied. The time delay is due to the presence of an incubation period during which the virus replicates enough in the mosquito so that the viruses can be transmitted by the mosquito to a human. The conditions for the existence of a Hopf bifurcation to limit cycle behavior are established. A theorem for determining whether for a given set of parameter values which satisfies the mathematical conditions, the system will actually undergo a transition from a stable state into a limit cycle state is established. It is found that for a set of realistic values of the parameters in the model, a Hopf bifurcation will not occur even when it is mathematically possible. For a set of unrealistic values of some of the parameters, it is shown that a Hopf bifurcation can occur. Numerical solutions using this set of values show the trajectory of two of the variables making a transition from a spiraling orbit to a limit cycle orbit.
MODELING TSUNAMI RUNUP DUE TO THE ANDAMAN TSUNAMI ALONG BEACHES IN MALAYSIA Teh Su Yean
Proceedings of ICMSA Vol 2, No 1 (2006): Applied Mathematics
Publisher : Proceedings of ICMSA

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Abstract

In an earlier paper, we modeled the propagation of waves across the deep oceans due to tsunami created from an earthquake that occurred around Banda Aceh, Indonesia on December 26, 2004 by means of an in-house tsunami propagation model TUNA-M2. Tsunami wave heights were simulated from the deep ocean up to offshore coasts at depths exceeding 50 m. In this paper, we develop an in-house model TUNA-RP, based upon the finite difference method, to guide the tsunami waves at these offshore locations onto the shallow coasts up to the beaches. The inputs for this model TUNA-RP are derived from the output of TUNA-M2 simulations, accounting for combinations of various source generation conditions reported. The synoptically simulated runup heights along certain beaches in Malaysia will be compared to the runup heights surveyed after the tsunami occurrence. Numerical stability and accuracy of the model will be briefly discussed in conjunction with other analytical and empirical formulations
IMPLEMENTATION OF TWO POINT BLOCK VARIABLE STEPS VARIABLE ORDER CODES FOR SOLVING ORDINARY DIFFERENTIAL EQUATIONS Zanariah Abdul Majid
Proceedings of ICMSA Vol 2, No 1 (2006): Applied Mathematics
Publisher : Proceedings of ICMSA

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Abstract

The efficient codes are developed for solving Initial Value Problems (IVPs) of first order Ordinary Differential Equations (ODEs) using variable step size and order. The codes will contain the 2-point one block fully implicit block method of order 5, the 2-point two block fully implicit block method of order 7 and the 2-point three block fully implicit block method of order 9. These methods will estimate the numerical solution at two equally spaced points simultaneously within a block. The performances of the codes will be compared in terms of maximum error, total number of steps and execution times with the code 2PVSO in Omar [7].
NUMERICAL COMPUTATION OF DIFFERENT ASPECTS OF 26 DECEMBER 2004 TSUNAMI ALONG THE PENANG ISLAND USING A CYLINDRICAL POLAR MODEL Md. Fazlul. Karim
Proceedings of ICMSA Vol 2, No 1 (2006): Applied Mathematics
Publisher : Proceedings of ICMSA

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Abstract

The tsunami of December 26, 2004 was devastating in its effect on the island of Penang. A numerical model based on the linear shallow-water equations in cylindrical polar coordinate system was discussed and the results presented in a previous study ( Roy and Izani, 2005). In this study we investigate the effects of using a more refined grid on the wave height distribution along the coastline of Penang. We also study the effect of changing the orientation of the source. Our studies show that the more refined grid is capable of generating wave heights in good agreement with observed data without excessively increasing the computation time. It is also found that orientation of the source have a significant effect on the wave heights.
GROUP CLASSIFICATION OF LINEAR SECOND-ORDER DELAY ORDINARY DIFFERENTIAL EQUATION Prapart Pue-on
Proceedings of ICMSA Vol 2, No 1 (2006): Applied Mathematics
Publisher : Proceedings of ICMSA

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Abstract

The linear delay ordinary differential equationy”(x) + a(x) y’(x) + b(x) y’(x −τ ) + c(x) y(x) + d(x) y(x −τ ) = g(x)is studied, where the coefficients a(x),b(x), c(x) and d(x) and function g(x) are arbitrary. In this manuscript, group analysis is applied to find equivalent symmetries of the equation.
VARIABLE ORDER VARIABLE STEPSIZE ALGORITHM FOR THE NUMERICAL SOLUTION OF DELAY DIFFERENTIAL EQUATIONS IN DIVIDED DIFFERENCE FORM Fuziyah bt Ishak
Proceedings of ICMSA Vol 2, No 1 (2006): Applied Mathematics
Publisher : Proceedings of ICMSA

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Abstract

A variable order variable stepsize algorithm for the numerical solution of delay differential equations is described. The algorithm is adapted from the algorithms developed by Suleiman [10] and Omar [8] for the numerical solution of ordinary differential equations. The algorithm is based on the variable step formulation of the Adams method in divided difference form. The predictor-corrector mode using Adams-Bashforth and Adams-Moulton formulae are implemented. This algorithm proves to be reliable, accurate and efficient. The results of four test examples are presented.

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