Zurni Omar

Parallel two-Point Explicit Block method for solving high-order Ordinary Differential Equations

The derivation of a new parallel two-Point Explicit Block (2PEB) method for solving dth-order Ordinary Differential Equations (ODEs) directly is presented. The computational advantages of using this technique over the conventional one-point method are discussed. Numerical results suggest that the parallel 2PEB method is superior when used for solving second-order ODEs directly with small step size.

Robust linear discriminant models to solve financial crisis in banking sectors

Linear discriminant analysis (LDA) is a widely-used technique in patterns classification via an equation which will minimize the probability of misclassifying cases into their respective categories. However, the performance of classical estimators in LDA highly depends on the assumptions of normality and homoscedasticity. Several robust estimators in LDA such as Minimum Covariance Determinant (MCD), S-estimators and Minimum Volume Ellipsoid (MVE) are addressed by many authors to alleviate the problem of non-robustness of the classical estimates. In this paper, we investigate on the financial crisis of the Malaysian banking institutions using robust LDA and classical LDA methods. Our objective is to distinguish the “distress” and “non-distress” banks in Malaysia by using the LDA models. Hit ratio is used to validate the accuracy predictive of LDA models. The performance of LDA is evaluated by estimating the misclassification rate via apparent error rate. The results and comparisons show that the robust est...

Physicochemical and rheological properties of titania and carbon nanotubes in a channel with changing walls: Investigation of critical points

Purpose The purpose of this paper is to investigate some multiple solutions for carbon nanotubes (CNTs) in a porous channel with changing walls. Moreover, the intention of the study is to examine the physicochemical and rheological properties of titania and CNTs. Design/methodology/approach The mathematical modeling is performed for the laws of conservation of mass, momentum and energy profiles. Governing partial differential equations are transformed into ordinary differential equations by applying suitable similarity transformation and then solved numerically with the help of shooting technique. Findings The effects of different physical parameters on the rheology of nanofluids are discussed graphically and numerically, in order to make the analysis more interesting. The present study revealed that multiple solutions of nanofluids in a channel with changing walls are obtained only for the case of suction. Originality/value Some new branches of the solution for nanofluids in a channel with changing walls are obtained in this research, which has never been reported before. Combined effects of physicochemical and rheology of titania and carbon nanotubes are investigated briefly. The effects of physical parameters on velocity and temperature profile are examined in detail which is more realistic than real-world problem.

A computationally efficient of robust mahalanobis distance based on MVV estimator

MCD is a well-known multivariate robust estimator. However, the computation of the estimator is not simple especially for large sample size due to the complexity of the objective function i.e. minimizing covariance determinant. Recently, an alternative objective function which is simpler and faster was introduced. The objective function is to minimize vector variance, which consequently will generate the estimator known as minimum vector variance (MVV). In this paper, a simulation study was conducted to compare the computational efficiency of the two estimators with regards to the number of operations in the computation of objective function and also iterations of the algorithm to convergence. The result showed that the computational efficiency of MVV is higher than MCD for small or large data set.

The efficiency of reweighted minimum vector variance

Minimum vector variance (MVV) is a new robust estimator which possesses the good properties as in minimum covariance determinant (MCD), but with better computational efficiency. However, the highly robust affine equivariant estimators with the best breakdown point commonly have to compensate with low statistical efficiency. Hence, to increase the efficiency while retaining the highest breakdown point, we proceed to improve the MVV estimators in the context of statistical efficiency via reweighted version (RMVV). Interestingly, the reweighted scheme was able to maintain the breakdown point of 0.5 and attained higher efficiency at the normal distribution.

Robust Hotelling Control Chart with Consistent Minimum Vector Variance

Recently, an alternative robust control chart based on a new robust estimator known as minimum vector variance (MVV) estimator, , was introduced in Phase II. was able to detect out-of-control signal and simultaneously control false alarm rate even as the dimension increased. However, the estimated UCLs of are large as compared to the traditional chart. In this study, we improved the MVV estimators in terms of consistency and bias. The result showed great improvement in the control limit values while maintaining its good performance in terms of false alarm and probability of detection.

Comparison of Block Methods with Different Step-Lengths for Solving Second Order Ordinary Differential Equations

This article considers the derivation and comparison of block methods with various step-lengths for solving second order initial value problems.The methods were developed via interpolation and collocation approach where a power series was employed as the interpolation equation.The developed methods using different step-lengths were applied to solve second order ordinary differential equations and the numerical solutions were then compared.In general, the results suggested that the higher step-length used, the better accuracy achieved.Further comparison with the existing methods also revealed that these block methods produced better accuracy when solving the same problems.

The impact of 2008 credit crisis on currency stability structure

The depreciation of many currencies over the world has retarded the economic development during 2008 credit crisis. The aim of this study is to detect the existence of changes in the currency stability structure by using a new covariance structure test known as S* statistics for high dimensional data involving 74 currencies. Comparisons were made between monthly data and overall data of 2008. Further analysis was conducted using network topology to visualise the pattern of structural changes and identifying which currencies affected by the crisis. The findings disclose that October currency structure has the utmost changes as compared to overall structure 2008. Forty one (or 55%) currencies were affected. The most affected currencies were Austrian schilling (ATS) and followed by Lebanese pound (LBP) and Mexican peso (MXN). These findings reflect the major impact of 2008 credit crisis on deterioration currencies performance.

Triple solutions of Casson fluid flow between slowly expanding and contracting walls

This study focuses on Casson fluid flow in a channel with slowly expanding and contracting walls. Main structures of partial differential equations were taken in the form of continuity, momentum and energy equations. Governing partial differential equations were converted into set of nonlinear ordinary differential equations by applying suitable similarity transformation and then solved numerically by employing shooting technique and triple solutions are obtained depending on Reynolds, Casson, expanding or contracting ratio and magnetic parameters considered.

A note on some solutions of micropolar fluid in a channel with permeable walls

Purpose The purpose of this paper is to investigate different branches of the solution of micropolar fluid in a channel with permeable walls. Moreover, the intention of the study is to examine the effect of different physical parameters on fluid flow. Design/methodology/approach The mathematical modeling is performed on the basis of law of conservation of mass, momentum and angular momentum. The governing partial differential equations were transformed into ordinary differential equations by applying suitable similarity transformation. Afterwards, the set of nonlinear ordinary differential equations was solved numerically by a shooting method. Findings The study reveals that various branches of the solution of the proposed problem exist only in the case of strong suction. Originality/value The investigation of new branches of the solution of non-Newtonian micropolar fluid is relatively difficult as far as the single solution is concern. This study explores the new branches of the solution of a micropolar fluid in a channel with suction/injection. Simultaneous effect of suction Reynolds number and vortex viscosity parameter on velocity and micro-rotation profile is examined for different branches of solution in order to make the analysis more interesting.