Implementation of the Explicit Group Iterative Method for Solving Image Blurring Problem using Non-Linear Diffusion Equations

Diffusion equations have been known to solve various image processing problems. This study employs the diffusion equations as the partial difference equations (PDEs)-based image processing techniques for image blurring which also can be refer as the process of image smoothing. The solutions of diffusion equations were obtained using the iterative algorithms and thereafter applied in the image blurring processes. The images were blurred without destroying the crucial information of an image that need to be preserve such as sharp edges, lines and shapes as the diffusion occurs inside the image locations, where the images with different sizes were tested. In terms of performance comparison, the standard point Gauss-Seidel and two-point Explicit Group (2-EG) methods were considered to produce the same quality image of classical point iterative method which is Jacobi. The numerical results showed that 2-EG iterative method capable to smooth the inner region of the images faster compared to the standard point iterative method. It was shown that the 2-EG iterative method more efficient in reducing the number of iterations and computational time than the standard point iterative method

First order piecewise collocation solution of Fredholm integral equation second kind by using gauss-seidel iteration

We determine the approximation solution of first-order piecewise via polynomial collocation with first-order Quadrature scheme on Fredholm integral equations of second kind. This discretization has derived the formation for solving piecewise approximation equation in which constructing the linear system. In order to get the approximation solutions, the Gauss-Seidel method has been stated as a linear solver in which its formulation has been constructed and implemented in this study. The combination of the iterative method of GS with the first-order piecewise polynomial via collocation with first-order Quadrature scheme has shown that performance of GS method is excel than Jacobi method in the matter of iterations number and completion time

Application of SOR iteration with nonlocal arithmetic discretization scheme for solving Burger’s equation

In this paper, the Burger’s equations have been approximated by using the second-order finite difference scheme and the half-sweep nonlocal arithmetic discretization scheme to construct the half-sweep generated linear system. Then, we investigate the applicable formulation of Half-sweep SuccessiveOver Relaxation (HSSOR) iterative method for solving this linear system. In order to verify the effectiveness of the HSSOR iterative method, this paper also included the Fullsweep Successive OverRelaxation (FSSOR) and Full-Sweep Gauss-Seidel (FSGS) iterative methods. The performance analysis of these three proposed iterative methods is illustrated by solving four proposed Burger’s problems. The numerical results illustrate the great performance of the HSSOR iterative method together with half-sweep nonlocal arithmetic discretization scheme to solve the Burger’s equations in senses of execution time and number of iterations

First order piecewise collocation solution of fredholm integral equation second type using SOR iteration

We evaluate the first-order approximation solution piecewise by firstorder polynomial collocation with Quadrature scheme on second-type Fredholm integral equations. This discretization derived the formulation to solve the first order piecewise approximation equation in which the linear system was built. The SOR method was described as a linear solver in which its formulation was constructed and applied in this study. In order to obtain the approximation solutions, the combination of SOR iterative method with the first-order piecewise polynomial by collocation with quadrature scheme has shown that performance of SOR method is superior than Jacobi method in terms of number of iterations and time of completion

The similarity finite difference solutions for two-dimensional parabolic partial differential equations via SOR iteration

This paper purposely attempts to solve two-dimensional (2D) parabolic partial differential equations (PDEs) using iterative numerical technique. Also, we determine the capability of proposed iterative technique known as Successive Over- Relaxation (SOR) iteration compared to Gauss–Seidel (GS) iteration for solving the 2D parabolic PDEs problem. Firstly, we transform the 2D parabolic PDEs into 2D elliptic PDEs then discretize it using the similarity finite difference (SFD) scheme in order to construct a SFD approximation equation. Then, the SFD approximation equation yields a large-scale and sparse linear system. Next, the linear system is solved by using the proposed iterative numerical technique as described before. Furthermore, the formulation and implementation of SOR iteration are also included. In addition to that, three numerical experiments were carried out to verify the performance of the SORiteration. Finally, the findings showthat the SORiteration performs better than the GS iteration with less iteration number and computational time

Semi-approximate solution for burgers’ equation using SOR iteration

In this article, we propose semi-approximate approach in finding a solution of Burgers’ equation which is one of the partial differential equations (PDEs).Without using the Newton method for linearization, we derive the approximation equation of the proposed problem by using second-order implicit scheme together with the semi-approximate approach. Then this approximation equation leads a huge scale and sparse linear system. Having this linear system, the Successive Overrelaxation (SOR) iteration will be performed as a linear solver. The formulation and execution of SOR iteration are included in this paper. This paper proposed four examples of Burgers’ equations to determine the performance of the suggested method. The test results discovered that the SOR iteration is more effective than GS iteration with less time of execution and minimum iteration numbers

Implicit solution of gs iteration with semi approximate approach for solving burgers’ equation

The aim of this study is to find semi-approximate solution of nonlinear Burgers’ equation based on the semi-approximate approach. To derive the approximation equation, the discretization of second-order implicit scheme has been used to discretize the proposed problem. To eliminate the nonlinear term of the proposed problems, semi-approximate approach is used to form a linear system which can be solved iteratively. Furthemore, numerical results of three proposed examples are included to examine the performance of Gauss-Seidel (GS) iteration compared to Jacobi iteration. The implementation of iteration with semi-approximate approach shown that GS iteration is more efficient than Jacobi iteration in aspect of iteration numbers and execution time

The Bruneian record of “Borneo Amber”: A regional review of fossil tree resins in the Indo-Australian Archipelago

In this study we intend to provide an overview on fossilized tree resins (amber) commonly found in Southeast Asia, more particularly in the Indo-Australian Archipelago (IAA). These remains are often referred in literature as “Indonesian amber”, “Borneo amber” or simply as “dammar”. They are very common in the region and the Brunei Sultanate is no exception as most of its Neogene sedimentary successions contain amber-rich layers. Although amber is a common fossil in the country and in northern Borneo, to our knowledge it has not been studied in great detail so far. Here we present an account on the “Borneo Ambers” from Brunei, regarding their stratigraphic origin, basic physical properties, their interaction with the biosphere and their botanical origin using Fourier-transform infrared spectroscopy (FTIR). Additionally, a number of ambers and modern tree resins were analysed for their carbon isotope composition and a few were tested with gas chromatography. We discuss the results in a regional and global context, in comparison with available data from the IAA. The ambers come from four different lithostratigraphic units with an age range of 12 to 3 million years (middle Miocene to Pliocene). Recently reworked ambers from the coast, ambers from younger alluvial deposits, and several modern tree resins from Dipterocarpaceae and Araucariaceae (Agathis borneensis) were also included in the study. The >60 FTIR analyses of modern and fossil specimens suggest that all the Brunei ambers were produced by trees of Dipterocarpaceae. There is no indication of Agathis in the fossil record, in agreement with their lower abundance in the forests of Borneo. Modern and fossil dipterocarp resins were found to be different based on the following criteria: (1) Different reactions to solubility, hot needle and UV tests with faster reaction time and less fluorescence for the modern ones; (2) Clear distinction based on certain FTIR absorbance band ratios, mostly by those that represent carboxylic acids and esters (e.g., ~1700 and 1243 cm-1); (3) Modern resin yielded on an average 3‰ lower δ13C values, (4) Gas chromatography data reflect maturation differences among the samples. Although there is some overlap in the chemical results between the two groups, generally all these differences reflect different maturation stages of the resinous material and point towards loss of low δ13C components from the organic structure of the resin. The minor timewise decreasing trend in average δ13C from the late middle Miocene to late Miocene can be explained by (1) gradual changes in local environmental conditions, and/or (2) increased amount of less mature specimens among the younger samples. In contrast, the highest obtained δ13C values were found in the youngest Pliocene ambers. Instead of maturation bias this can be linked to environmental factors such as cooler-drier climate with increased seasonality, probably reflecting the onset of the northern hemisphere glaciation

Low temperature resistivity of the rare earth diborides (Er, Ho, Tm)B2

The discovery of superconductivity in MgB2 sparked much interest in the diborides and led to further discoveries in this class of materials. Attention has focussed on the transitions metal diborides and the rare-earth diborides have remained sparsely investigated. Here we present electrical transport in polycrystalline samples of ErB2, TmB2 and HoB2 as a function of temperature down to 0.1 K. Particularly interesting is the large difference in the temperature dependence of resistivity, above and below the clear magnetic ordering temperature of 13.8, 9 and 7.5 K for ErB2, HoB2 and TmB2 respectively