Kim Gaik Tay

New Richardson’s extrapolation spreadsheet calculator using VBA programming for numerical differentiations

In this paper, we have further improved the limitations of our previous two Richardson’s extrapolation spreadsheet calculators for computing differentiations numerically. The new feature in this new Richardson’s extrapolation spreadsheet calculator is fully automated up to any level based on the stopping criteria using VBA programming. The new version is more flexible because it is controlled by programming. Furthermore, it reduces computational time and CPU memory.

Numerical Solution of the Gardner Equation

The Gardner equation is commonly used to describe wave propagation in weakly nonlinear dispersive medium. The Gardner equation has a higher order nonlinear term, which could make the numerical calculation inaccurate. In this paper, the Gardner equation is solved using two numerical methods, i.e., the method of lines and pseudospectral method. The efficiency and accuracy of both methods were studied. Our results show that both methods are accurate and efficient methods to solve the Gardner equation. By comparing the accuracy of both the methods, the method of lines performs better than pseudospectral method most of the time.

Solving Nonlinear Schrodinger Equation with Variable Coefficient Using Homotopy Perturbation Method

In this paper, the application of the homotopy perturbation method (HPM) to the nonlinear Schrodinger equation with variable coefficient (NLSV) is presented to obtain approximate analytical solution. The procedure of the method is systematically illustrated. The result derived by this method is then compared with the progressive wave solution to verify the accuracy of the HPM solution. The solution obtained by the HPM is an infinite series for appropriate initial condition that can be expressed in a closed form to the exact solution. The absolute errors of the HPM solution of the NLSV equation with the progressive wave solution will later be carried out using the MAPLE program. The results of the HPM solution are of high accuracy, verifying that the method is indeed effective and promising. The HPM is found to be a powerful mathematical tool which can be used to solve nonlinear partial differential equations.

Optimal control of a coupled tanks system with model-reality differences

In this paper, an efficient computational approach is proposed to optimize and control a coupled tanks system. Since the dynamics of the coupled tanks system is nonlinear, determination of the optimal water level in the tanks could be formulated as an optimal control problem for a useful operation decision. For simplicity, the linear model of the coupled tanks system is suggested to give the true operating height of the coupled tanks. In our approach, the adjustable parameter is added into the model used. The aim is to measure the differences between the real plant and the model used repeatedly during the computation procedure. In this way, the optimal solution of the model used can be updated iteratively. On this basis, system optimization and parameter estimation are integrated. At the end of the iteration procedure, the converged solution approximates to the correct optimal solution of the original optimal control problem, in spite of model-reality differences. For illustration, the numerical parameter...

Optical Soliton Simulation in Optical Fibers by OptiSystem

Fiber optic communication is often known to offer higher frequency transmission of signals with greater bit rate and larger data carrying capacity over a long distance with lower loss and interference as compared to copper wire electrical communication. However, several factors that would affect the performance of an optical fiber transmission are such as group velocity dispersion (GVD), fiber loss and also self-phase modulation (SPM). In this paper, the effects of GVD, SPM, optical soliton formation and fiber loss are simulated using OptiSystem 14. It is found that GVD broaden pulse in temporal domain without modifying its spectrum. Meanwhile, SPM creates chirp in spectrum with its temporal profile maintained. This work concluded that a balance between the GVD and SPM is essential to form solitonthat is able to travel for a long distance without being distorted. It is also found that the decrease in the amplitude of the soliton is dependent on the fiber loss and this decay in the signal increases with the propagation distance.

The influence of dispersion slope to the higher-order dispersion coefficients for highly-nonlinear fibers

The highly-nonlinear fiber is the ideal gain medium for many applications particularly because its dispersion can be easily engineered. However, the modification of the fiber dispersion will affect the higher-order dispersion coefficients. Hence, this paper investigates the effect of highly-nonlinear dispersion-shifted fiber dispersion profile on the higher-order dispersion coefficients which are the fourth-order and sixth-order dispersion coefficients. The dispersion profile was modified by varying the slope at zero-dispersion wavelength. The fourth-order dispersion coefficient exhibits changes from positive to negative value as the slope at zero-dispersion wavelength is getting higher. Meanwhile, sixth-order dispersion coefficient remains with the positive value even though it shows the reduction as the slope is increased, however it will eventually become negative when the dispersion is high enough. In short, the values of both fourth-order and sixth-order dispersion coefficients at zero-dispersion wavelength decrease when the slope increases.At the request of all authors of the paper, an updated version of this article was published on 13 October 2017. The original version supplied to AIP Publishing had an incorrect affiliation for R. Talib. The affiliation for R. Talib was changed from 3Shiraz University of Technology to 1Universiti Tun Hussein Onn Malaysia. This has been corrected in the updated and re-published version.The highly-nonlinear fiber is the ideal gain medium for many applications particularly because its dispersion can be easily engineered. However, the modification of the fiber dispersion will affect the higher-order dispersion coefficients. Hence, this paper investigates the effect of highly-nonlinear dispersion-shifted fiber dispersion profile on the higher-order dispersion coefficients which are the fourth-order and sixth-order dispersion coefficients. The dispersion profile was modified by varying the slope at zero-dispersion wavelength. The fourth-order dispersion coefficient exhibits changes from positive to negative value as the slope at zero-dispersion wavelength is getting higher. Meanwhile, sixth-order dispersion coefficient remains with the positive value even though it shows the reduction as the slope is increased, however it will eventually become negative when the dispersion is high enough. In s...

The influence of fiber parameters to the fiber optical parametric amplifier gain spectrum

Using the theory derived from the three coupled amplitude equations which frequently used to explain the interaction of the fields in a fiber optical parametric amplifier, the parametric gain was simulated to investigate the influence of fiber parameters to the gain spectrum. Results show that under a certain condition, the selected fiber parameters such as fiber length, pump wavelength, pump power and dispersion slope have huge contributions to the parametric gain and amplification bandwidth. In addition, fourth-order dispersion coefficient parameter needs to be carefully altered since it relates to the linear phase-mismatch. In this paper, the obtained maximum gain is about 45 dB and the bandwidth is 80 nm. Most of the expressions involved in this simulation are connected to each other, which mathematically explain the difference behavior of gain profile when the fiber parameters were manipulated.

Reflectance spectroscopy system for noninvasive prediction of skin bilirubin concentration related parameter

Bilirubin level increased when ones liver is unable to remove bilirubin sufficiently from the blood. The conventional methods used for monitoring and measuring the bilirubin level are tedious, time consuming and may be invasive in nature. This research employed reflectance optical system to collect spectroscopic data of light reflected from skin. Modified Lambert Beer model is used to predict ones skin bilirubin level using a priori information of bilirubin absorptivity in the wavelength range of 440–490 nm. This study found a lower skin bilirubin level of 1.0043 ± 0.02 AU (arbitrary unit) amongst the renal disease volunteers compared to 1.0165 ± 0.0197 AU for healthy volunteers. Meanwhile, no significant changes in the value were observed for populations with different skin color. The absolute difference in the mean and standard deviation of these values was calculated as 0.005 ± 0.03 AU. This preliminary study concluded that the developed system and strategy may be used as an alternative means to assess ones skin bilirubin level and hence a diagnostic tool for clinical application such as renal disease, jaundice and hepatitis.

Numerical simulation of undular bore evolution with Chezy friction

This paper studies and simulates numerically the evolution of undular bore under the effect of damping in the framework of the perturbed extended Korteweg-de Vries equation. Here, we consider Chezy frictional term to be the damping term in the perturbed extended Korteweg-de Vries equation. Numerical simulations show that under the influence of the friction, the undular bore with thick leading wave will transform into KdV-like solitary wave as the leading wave of the undular bore. The amplitude of the “thick” leading wave will remain the same for some time even though there is dissipation effect.

Crank-Nicolson implicit method for the nonlinear Schrodinger equation with variable coefficient

In the present work, the Crank-Nicolson implicit scheme for the numerical solution of nonlinear Schrodinger equation with variable coefficient is introduced. The Crank-Nicolson scheme is second order accurate in time and space directions. The stability analysis for the Crank-Nicolson method is investigated and this method is shown to be unconditionally stable. The numerical results obtained by the Crank-Nicolson method are presented to confirm the analytical results for the progressive wave solution of nonlinear Schrodinger equation with variable coefficient.