Numerical Solution for Solving Space-Fractional Diffusion Equations using Half-sweep Gauss-seidel Iterative Method

The main purpose of this paper is to examine theeffectiveness of Half-Sweep Gauss-Seidel (HSGS) method forSpace-Fractional diffusion equations. The Caputo’s derivativeand implicit finite difference scheme will be used to discretizelinear space-fractional equation of the first order to constructsystem linear equation. The basic formulation and application ofthe HSGS iterative method are also presented. Two numericalexamples and comparison with other iterative methods showsthat the present method is effective. Based on computationalnumerical result, the solution obtained by proposed iterativemethod is in excellent agreement, it can be concluded that theproposed iterative method is superior to the Full-Sweep Gauss-Seidel (FSGS) iterative metho

Application of the Central-Difference with Half-Sweep Gauss-Seidel Method for Solving First Order Linear Fredholm Integro-Differential Equations

The objective of this paper is to analyse the application of the Half-Sweep Gauss-Seidel (HSGS) method by using the Half-sweep approximation equation based on central difference (CD) and repeated trapezoidal (RT) formulas to solve linear fredholm integro-differential equations of first order. The formulation and implementation of the Full-Sweep Gauss-Seidel (FSGS) and Half- Sweep Gauss-Seidel (HSGS) methods are also presented. The HSGS method has been shown to rapid compared to the FSGS methods. Some numerical tests were illustrated to show that the HSGS method is superior to the FSGS method

The Half-Sweep Iterative Alternating Decomposition Explicit (HSIADE) method for diffusion equation

The primary goal of this paper is to apply the Half-Sweep Iterative Alternating Decomposition Explicit (HSIADE) method for solving one-dimensional diffusion problems. The formulation of the HSIADE method is also derived. Some numerical experiments are conducted that to verify the HSIADE method is more efficient than the Full-Sweep metho

SIMULATING SEISMIC WAVE PROPAGATION IN TWO-DIMENSIONAL MEDIA USING DISCONTINUOUS SPECTRAL ELEMENT METHODS

We introduce a discontinuous spectral element method for simulating seismic wave in 2- dimensional elastic media. The methods combine the flexibility of a discontinuous finite element method with the accuracy of a spectral method. The elastodynamic equations are discretized using high-degree of Lagrange interpolants and integration over an element is accomplished based upon the Gauss-Lobatto-Legendre integration rule. This combination of discretization and integration results in a diagonal mass matrix and the use of discontinuous finite element method makes the calculation can be done locally in each element. Thus, the algorithm is simplified drastically. We validated the results of one-dimensional problem by comparing them with finite-difference time-domain method and exact solution. The comparisons show excellent agreement