In the current paper, we present a generalized symbolic thomas algorithm, that never suffers from breakdown, for solving the opposite-bordered tridiagonal (OBT) linear systems. The algorithm uses a fill-in matrix fact...
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In the current paper, we present a generalized symbolic thomas algorithm, that never suffers from breakdown, for solving the opposite-bordered tridiagonal (OBT) linear systems. The algorithm uses a fill-in matrix factorization and can solve an OBT linear system in 0(n) operations. Meanwhile, an efficient method of evaluating the determinant of an opposite-bordered tridiagonal matrix is derived. The computational costs of the proposed algorithms are also discussed. Moreover, three numerical examples are provided in order to demonstrate the performance and effectiveness of our algorithms and their competitiveness with some already existing algorithms. All of the experiments are performed on a computer with the aid of programs written in Matlab. (C) 2015 Elsevier B.V. All rights reserved.
We propose a normalized time-fractional Fokker-Planck equation (TFFPE). A finite ence method is used to develop a computational method for solving the equation, system's dynamics are investigated through computati...
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We propose a normalized time-fractional Fokker-Planck equation (TFFPE). A finite ence method is used to develop a computational method for solving the equation, system's dynamics are investigated through computational simulations. The proposed demonstrates accuracy and efficiency in approximating analytical solutions. Numerical validate the method's effectiveness and highlight the impact of various fractional the dynamics of the normalized time-fractional Fokker-Planck equation. The numerical emphasize the significant impact of different fractional orders on the temporal evolution the system. Specifically, the computational results demonstrate how varying the order influences the diffusion process, with lower orders exhibiting stronger memory and slower diffusion, while higher orders lead to faster propagation and a transition classical diffusion behavior. This work contributes to the understanding of fractional and provides a robust tool for simulating time-fractional systems.
We introduce an asymptotic approximate algorithm for solving nearly tridiagonal quasi-Toeplitz linear systems. When addressing low-rank perturbations of a tridiagonal Toeplitz matrix system based on the Sherman-Morris...
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We introduce an asymptotic approximate algorithm for solving nearly tridiagonal quasi-Toeplitz linear systems. When addressing low-rank perturbations of a tridiagonal Toeplitz matrix system based on the Sherman-Morrison-Woodbury formula (or Woodbury identity), conventional methods require solving at least two simpler systems. The proposed algorithm overcomes this limitation by providing an explicit asymptotic formula for one of these systems. This asymptotic approximation enables a rapid resolution of the original system with minimal additional computation. To validate the accuracy and efficiency of the proposed algorithm, we conduct numerical experiments on two cases, comparing the results with those of existing methods. The results demonstrate that the proposed algorithm significantly reduces computation time while maintaining accuracy compared to the existing methods.
Cyclic tridiagonal matrices, a specific subclass of quasi-tridiagonal matrices, frequently arise in theoretical and computational chemistry. This paper addresses the solution of cyclic tridiagonal linear systems with ...
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Cyclic tridiagonal matrices, a specific subclass of quasi-tridiagonal matrices, frequently arise in theoretical and computational chemistry. This paper addresses the solution of cyclic tridiagonal linear systems with coefficient matrices that are subdiagonally dominant, superdiagonally dominant and weakly diagonally dominant. For the subdiagonally dominant case, we perform an elementary transformation to convert the matrix into a block 2-by-2 form, then solve the system using block LU factorization. For the superdiagonally dominant and weakly diagonally dominant cases, we extend this approach using block LU factorization and matrix similarity transformations. Our proposed algorithms outperform existing methods in terms of floating-point operations, memory storage, and data transmission. Numerical experiments, implemented in MATLAB, demonstrate the accuracy and efficiency of the proposed algorithms.
The chemical-potential multiphase lattice Boltzmann method (CP-LBM) has the advantages of satisfying the thermodynamic consistency and Galilean invariance, and it realizes a very large density ratio and easily express...
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The chemical-potential multiphase lattice Boltzmann method (CP-LBM) has the advantages of satisfying the thermodynamic consistency and Galilean invariance, and it realizes a very large density ratio and easily expresses the surface wettability. Compared with the traditional central difference scheme, the CP-LBM uses the thomas algorithm to calculate the differences in the multiphase simulations, which significantly improves the calculation accuracy but increases the calculation complexity. In this study, we designed and implemented a parallel algorithm for the chemical-potential model on a graphic processing unit (GPU). Several strategies were used to optimize the GPU algorithm, such as coalesced access, instruction throughput, thread organization, memory access, and loop unrolling. Compared with dual-Xeon 5117 CPU server, our methods achieved 95 times speedup on an NVIDIA RTX 2080Ti GPU and 106 times speedup on an NVIDIA Tesla P100 GPU. When the algorithm was extended to the environment with dual NVIDIA Tesla P100 GPUs, 189 times speedup was achieved and the workload of each GPU reached 96%.
The efficiency of solving computationally partial differential equations can be profoundly highlighted by the creation of precise,higher-order compact numerical scheme that results in truly outstanding accuracy at a g...
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The efficiency of solving computationally partial differential equations can be profoundly highlighted by the creation of precise,higher-order compact numerical scheme that results in truly outstanding accuracy at a given *** objective of this article is to develop a highly accurate novel algorithm for two dimensional non-linear Burgers Huxley(BH)*** proposed compact numerical scheme is found to be free of superiors approximate oscillations across discontinuities,and in a smooth ow region,it efciently obtained a high-order *** particular,two classes of higherorder compact nite difference schemes are taken into account and compared based on their computational *** stability and accuracy show that the schemes are unconditionally stable and accurate up to a two-order in time and to six-order in ***,algorithms and data tables illustrate the scheme efciency and decisiveness for solving such non-linear coupled *** is scaled in terms of L_(2) and L_(∞) norms,which validate the approximated results with the corresponding analytical *** investigation of the stability requirements of the implicit method applied in the algorithm was carried *** agreement was constructed under indistinguishable computational *** proposed methods can be implemented for real-world problems,originating in engineering and science.
The principle goal of the paper is to present proficient limited contrast finite difference schemes to execute on the nonlinear coupled partial differential system which emulate the overseeing differential framework. ...
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The principle goal of the paper is to present proficient limited contrast finite difference schemes to execute on the nonlinear coupled partial differential system which emulate the overseeing differential framework. In this paper, more consideration is given to the exactness and security of the proposed numerical schemes by review consistency and union of the arrangement which can be seen from figures and information tables. For the nonlinear differential system, mesh independent results are expensive which are accommodated by the generation of block tridiagonal matrix structures (inherent properties of schemes) which are measured in terms of L-2 & L-infinity norms which lead to a superb concurrence with the investigative arrangement.
Purpose The purpose of this paper is to provide an efficient and robust second-order monotone hybrid scheme for singularly perturbed delay parabolic convection-diffusion initial boundary value problem. Design/methodol...
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Purpose The purpose of this paper is to provide an efficient and robust second-order monotone hybrid scheme for singularly perturbed delay parabolic convection-diffusion initial boundary value problem. Design/methodology/approach The delay parabolic problem is solved numerically by a finite difference scheme consists of implicit Euler scheme for the time derivative and a monotone hybrid scheme with variable weights for the spatial derivative. The domain is discretized in the temporal direction using uniform mesh while the spatial direction is discretized using three types of non-uniform meshes mainly the standard Shishkin mesh, the Bakhvalov-Shishkin mesh and the Gartland Shishkin mesh. Findings The proposed scheme is shown to be a parameter-uniform convergent scheme, which is second-order convergent and optimal for the case. Also, the authors used the thomas algorithm approach for the computational purposes, which took less time for the computation, and hence, more efficient than the other methods used in literature. Originality/value A singularly perturbed delay parabolic convection-diffusion initial boundary value problem is considered. The solution of the problem possesses a regular boundary layer. The authors solve this problem numerically using a monotone hybrid scheme. The error analysis is carried out. It is shown to be parameter-uniform convergent and is of second-order accurate. Numerical results are shown to verify the theoretical estimates.
In this article, B-spline-based collocation method is employed to approximate the usual and modified Rosenau-RLW nonlinear equations. The weighted extended B-spline (WEB-spline) is used as the modified form of B-splin...
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In this article, B-spline-based collocation method is employed to approximate the usual and modified Rosenau-RLW nonlinear equations. The weighted extended B-spline (WEB-spline) is used as the modified form of B-spline as the usual B-splines fail to obey the Dirichlet boundary conditions. The WEB method is more general method that allows to discretize the domain into finite number of elements not necessarily start from the boundary points of the domain. Our method omits the linearization process of the nonlinear partial differential equation (PDE). Different cases are discussed by setting the parameter p=2,3,4, and 6 that appears in Rosenau-RLW equations. The error estimation is calculated, which gives good agreement of the exact solution.
Numerical modeling of RF magnetron sputtering discharge of argon plasma properties, using a one-dimensional time-dependent fluid model in presence of the magnetic field, has been developed. The model is based on conti...
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Numerical modeling of RF magnetron sputtering discharge of argon plasma properties, using a one-dimensional time-dependent fluid model in presence of the magnetic field, has been developed. The model is based on continuity equation and electron temperature equation coupled with Poisson's equation. The electron mobility depends on magnetic field and the electron diffusivity is assumed to be dependent of electron energy by Einstein's relation. The flux is calculated by Scharfetter and Gummel schemes. Numerical simulations were resolved by using the Finite Volume Method (FVM) and the thomas algorithm. The obtained results for the electrical properties, electron and ion densities, electrical potential, electric field and electron temperature, are in good agreement with previous works. A parametric study varying the magnetic field intensity on the discharge properties is done. (C) 2018 Production and hosting by Elsevier B.V. on behalf of King Saud University.
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