Determination of finite-difference weights using scaled binomial windows

The finite-difference method evaluates a derivative through a weighted summation of function values from neighboring grid nodes. Conventional finite-difference weights can be calculated either from Taylor series expansions or by Lagrange interpolation polynomials. The finite-difference method can be interpreted as a truncated convolutional counterpart of the pseudospectral method in the space domain. For this reason, we also can derive finite-difference operators by truncating the convolution series of the pseudospectral method. Various truncation windows can be employed for this purpose and they result in finite-difference operators with different dispersion properties. We found that there exists two families of scaled binomial windows that can be used to derive conventional finite-difference operators analytically. With a minor change, these scaled binomial windows can also be used to derive optimized finite-difference operators with enhanced dispersion properties.

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Simulation of the Seismic Response of Two Different Thick Deposition Layers with Hybrid PSM/FDM Method

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.353-356.1858 ◽

2013 ◽

Vol 353-356 ◽

pp. 1858-1866

Author(s):

Wu Jian Yan ◽

Yu Cheng Shi

Keyword(s):

Finite Difference ◽

Finite Difference Method ◽

Ground Motion ◽

Difference Method ◽

Strong Ground Motion ◽

Pseudospectral Method ◽

Wavefield Simulation ◽

The Finite Difference Method ◽

Seismic Wavefield ◽

Strong Ground

In this paper, we simulated two-dimension numerical on the strong ground motion through the hybrid scheme based on the pseudo-spectral method (PSM) and finite difference method (FDM). We based on the same focal depth, and 2 different thick deposition layers are used as models to analyze the relationship between site situation and the peak displacement of strong ground motion. The results show that the hybrid PSM/FDM method for seismic wavefield simulation combines with advantages of the pseudospectral method and the finite difference method and makes up for the disadvantage of the pseudospectral method and the finite difference method, so this method can process well the calculation of the discontinuous medium surface, then the calculation accuracy is similar to the pseudospectral method. Through the wavefield simulation it is known that the range of the seismic wavefield the peak ground displacement (PGD) of the thicker deposition is larger and the influence of the secondary surface wave at the basin edge is more obvious. The thicker deposition amplitude of strong ground motion in the basin is larger and the duration is longer, and the reflected wave of which is more obvious and stronger. However, the difference of the site condition has little influence to strong ground motion in the horizontal direction.

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1D Generalised Burgers-Huxley: Proposed Solutions Revisited and Numerical Solution Using FTCS and NSFD Methods

Frontiers in Applied Mathematics and Statistics ◽

10.3389/fams.2021.773733 ◽

2022 ◽

Vol 7 ◽

Author(s):

Appanah R. Appadu ◽

Yusuf O. Tijani

Keyword(s):

Exact Solution ◽

Finite Difference ◽

Finite Difference Method ◽

Boundary Conditions ◽

Difference Scheme ◽

Numerical Solution ◽

Difference Method ◽

Huxley Equation ◽

The Finite Difference Method ◽

A Minor

In this paper, we obtain the numerical solution of a 1-D generalised Burgers-Huxley equation under specified initial and boundary conditions, considered in three different regimes. The methods are Forward Time Central Space (FTCS) and a non-standard finite difference scheme (NSFD). We showed the schemes satisfy the generic requirements of the finite difference method in solving a particular problem. There are two proposed solutions for this problem and we show that one of the proposed solutions contains a minor error. We present results using FTCS, NSFD, and exact solution as well as show how the profiles differ when the two proposed solutions are used. In this problem, the boundary conditions are obtained from the proposed solutions. Error analysis and convergence tests are performed.

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