Showing papers on "Finite difference coefficient published in 2019"
Book•
04 Nov 2019
TL;DR: In this paper, the authors consider linear initial value problems, Sturm-Liouville problems and related inequalities in several independent variables, including difference inequalities and boundary value problems for linear systems and nonlinear systems.
Abstract: Preliminaries linear initial value problems miscellaneous difference equations difference inequalities qualitative properties of solutions of difference systems qualitative properties of solutions of higher order difference equations qualitative properties of solutions of neutral difference equations boundary value problems for linear systems boundary value problems for nonlinear systems miscellaneous properties of solutions of higher order linear difference equations boundary value problems for higher order difference equations Sturm-Liouville problems and related inequalities difference inequalities in several independent variables.
939 citations
TL;DR: In this article, an unconditionally stable compact finite difference scheme for the solution of linear convection-diffusion equation is proposed, where second derivative approximations of unknowns are eliminated with the unknowns itself and their first derivative approximation while retaining the fourth order accuracy and tri-diagonal nature of the scheme.
Abstract: In this paper, an unconditionally stable compact finite difference scheme for the solution of linear convection–diffusion equation is proposed. In the proposed scheme, second derivative approximations of the unknowns are eliminated with the unknowns itself and their first derivative approximations while retaining the fourth order accuracy and tri-diagonal nature of the scheme. Proposed compact finite difference scheme which is fourth order accurate in spatial variable and second or lower order accurate in temporal variable depending on the choice of weighted time average parameter is applied to Asian option partial differential equation. A diagonally dominant system of linear equation is obtained from the proposed scheme which can be efficiently solved. Two numerical examples are given to demonstrate the efficiency and accuracy of the proposed compact finite difference scheme.
18 citations
TL;DR: In this paper, the authors introduce the mathematical modeling of American put option under the fractional Black-Scholes model, which leads to a free boundary problem, and then the free boundary (optimal exercise boundary) that is unknown, is found by the quasi-stationary method that causes American put options problem to be solvable.
Abstract: We introduce the mathematical modeling of American put option under the fractional Black–Scholes model, which leads to a free boundary problem. Then the free boundary (optimal exercise boundary) that is unknown, is found by the quasi-stationary method that cause American put option problem to be solvable. In continuation we use a finite difference method for derivatives with respect to stock price, Grunwal Letnikov approximation for derivatives with respect to time and reach a fractional finite difference problem. We show that the set up fractional finite difference problem is stable and convergent. We also show that the numerical results satisfy the physical conditions of American put option pricing under the FBS model.
13 citations
25 Dec 2019
TL;DR: Ma et al. as discussed by the authors proposed a fourth-order finite-difference scheme for modeling elastic wave in frequency-domain, which can provide stable numerical solution with fewer number of grid points per wavelength.
Abstract: Simulation of elastic wave propagation is an important method for oil and gas exploration. Accuracy and efficiency of elastic wave simulation in complex geological environment are always the focus issue. In order to improve the accuracy and efficient in numerical modeling of elastic modeling, a staggered grid fourth-order finite-difference scheme of modeling elastic wave in frequency-domain is developed, which can provide stable numerical solution with fewer number of grid points per wavelength. The method is implemented on first-order velocity-stress equation and a parsimonious spatial staggered-grid with fourth-order approximation of the first-order derivative operator. Numerical tests show that the accuracy of the fourth-order staggered-grid stencil is superior to that of the mixed-grid and other conventional finite difference stencils, especially in terms of shear-wave phase velocity. Measures of mass averaging acceleration and optimization of finite difference coefficients are taken to improve the accuracy of numerical results. Meanwhile, the numerical accuracy of the finite difference scheme can be further improved by enlarging the mass averaging area at the price of expanding the bandwidth of the impedance matrix that results in the reduction of the number of grid points to 3 per shear wavelength and computer storage requirement in simulation of practical models. In our scheme, the phase velocities of compressional and shear wave are insensitive to Poisson's ratio that does not occur to conventional finite difference scheme in most cases, and also the elastic wave modeling can degenerate to acoustic case automatically when the medium is pure fluid or gas. Furthermore, the staggered grid scheme developed in this study is suitable for modeling waves propagating in media with coupling fluid-solid interfaces that are not resolved very well for previous finite difference method. Cited as : Ma, C., Gao, Y., Lu, C. Numerical modeling of elastic wave in frequency-domain by using staggered grid fourth-order fifinite-difference scheme. Advances in Geo-Energy Research, 2019, 3(4): 410-423, doi: 10.26804/ager.2019.04.08
4 citations
Patent•
17 Jul 2019
TL;DR: In this paper, the authors describe methods for efficient wavefield solutions, the methods including defining a wave equation as a linear portion and as a nonlinear portion; and solving the wave equation via an iterative process.
Abstract: Embodiments of the present disclosure describe methods for efficient wavefield solutions, the methods including defining a wave equation as a linear portion and as a nonlinear portion; and solving the wave equation via an iterative process, the iterative process including, at each iteration, performing LU decomposition before solving the nonlinear portion, or obtaining best finite difference coefficients by solving an optimization equation.