Topic
Finite difference method
About: Finite difference method is a research topic. Over the lifetime, 21603 publications have been published within this topic receiving 468852 citations. The topic is also known as: Finite-difference methods & FDM.
Papers published on a yearly basis
1 / 2
Papers
1 Jan 2010
TL;DR: The present meshless formulation is very effective for the modeling and simulation of the ASDE and should have good potential in development of a robust simulation tool for problems in engineering and science which are governed by the various types of fractional differential equations.
Abstract: Recently, the numerical modelling and simulation for anomalous subdiffusion equation (ASDE), which is a type of fractional partial differential equation( FPDE) and has been found with widely applications in modern engineering and sciences, are attracting more and more attentions. The current dominant numerical method for modelling ASDE is Finite Difference Method (FDM), which is based on a pre-defined grid leading to inherited issues or shortcomings. This paper aims to develop an implicit meshless approach based on the radial basis functions (RBF) for numerical simulation of the non-linear ASDE. The discrete system of equations is obtained by using the meshless shape functions and the strong-forms. The stability and convergence of this meshless approach are then discussed and theoretically proven. Several numerical examples with different problem domains are used to validate and investigate accuracy and efficiency of the newly developed meshless formulation. The results obtained by the meshless formulations are also compared with those obtained by FDM in terms of their accuracy and efficiency. It is concluded that the present meshless formulation is very effective for the modeling and simulation of the ASDE. Therefore, the meshless technique should have good potential in development of a robust simulation tool for problems in engineering and science which are governed by the various types of fractional differential equations.
80 citations
TL;DR: In this paper, an analytical and numerical thermal analysis for melting and consolidating impregnated composite tapes in the presence of a localized heat source is presented, which leads to the prediction of the processing window for a given tape-laying configuration.
Abstract: This paper presents analytical and numerical thermal analysis for melting and consolidating impregnated composite tapes in the presence of a localized heat source. This analysis also leads to the prediction of the processing window for a given tape-laying configuration. Heat of melting/solidification is included in the form of a heat generation term. A separation of variables method is employed to solve the governing equations ana lytically. In the numerical analysis, the governing equations are discretized using a non uniform mesh and are solved using a finite difference approach. The processing parame ters, such as consolidation speed, heat intensity, heat source width, etc., as well as material properties are incorporated within the analysis. The results show large thermal gradients in the vicinity of the consolidation point. The error between the analytical solu tion and the numerical result is found to be 3 % for the maximum temperature, and the maximum error for the temperature over the entire domai...
80 citations
TL;DR: A two-grid block-centered finite difference method is proposed for solving the two-dimensional Darcy--Forchheimer model describing non-Darcy flow in porous media and optimal order error estimates for pressure and velocity in discrete $L^2$ norms are obtained.
Abstract: A two-grid block-centered finite difference method is proposed for solving the two-dimensional Darcy--Forchheimer model describing non-Darcy flow in porous media. To construct the two-grid method we modify the original nonlinear elliptic operator of Darcy--Forchheimer flow to a twice continuously differentiable one by introducing a small and positive parameter $\varepsilon$. By using the two-grid method, solving a nonlinear equation on a fine grid is reduced to solving a nonlinear equation on a coarse grid together with solving a linear equation on a fine grid. Optimal order error estimates for pressure and velocity in discrete $L^2$ norms are obtained. Some numerical examples are given to show the accuracy and efficiency of the presented method.
80 citations
1 Jun 1982
80 citations
TL;DR: In this paper, a finite difference approach for valuing a discretely sampled variance swap within a Black-Scholes framework is presented, which incorporates the observed volatility skew and is capable of handling various definitions of the variance.
Abstract: We develop here a finite difference approach for valuing a discretely sampled variance swap within a Black-Scholes framework. This approach incorporates the observed volatility skew and is capable of handling various definitions of the variance. It is benchmarked against Monte-Carlo simulation in the presence of a volatility skew and is shown to provide extremely accurate values for a variance swap. Our method is based on decomposing the problem of valuing a variance swap into a set of one-dimensional PDE problems, each of which is then solved using a finite difference method.
80 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 53 |
| 2024 | 136 |
| 2023 | 170 |
| 2022 | 357 |
| 2021 | 733 |
| 2020 | 690 |