Hybrid Spectral Difference Methods for Elliptic Equations on Exterior Domains with the Discrete Radial Absorbing Boundary Condition
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DOI: 10.1007/s10915-017-0570-0
Abstract: The hybrid spectral difference methods (HSD) for the Laplace and Helmholtz equations in exterior domains are proposed. We consider the fictitious domain method with the absorbing boundary conditions (ABCs). The HSD method is a finite… read more here.
Keywords: difference; equations exterior; difference methods; discrete radial ... See more keywords
Higher-Order Adaptive Finite Difference Methods for Fully Nonlinear Elliptic Equations
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DOI: 10.1007/s10915-017-0586-5
Abstract: We introduce generalised finite difference methods for solving fully nonlinear elliptic partial differential equations. Methods are based on piecewise Cartesian meshes augmented by additional points along the boundary. This allows for adaptive meshes and complicated… read more here.
Keywords: fully nonlinear; difference; difference methods; higher order ... See more keywords
High-Order Compact Difference Methods for Caputo-Type Variable Coefficient Fractional Sub-diffusion Equations in Conservative Form
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DOI: 10.1007/s10915-018-0647-4
Abstract: A set of high-order compact finite difference methods is proposed for solving a class of Caputo-type fractional sub-diffusion equations in conservative form. The diffusion coefficient of the equation may be spatially variable, and the proposed… read more here.
Keywords: order; diffusion; difference methods; order compact ... See more keywords
Exponential finite difference methods for solving Newell–Whitehead–Segel equation
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DOI: 10.1007/s40065-020-00280-3
Abstract: This work presents two different finite difference methods to compute the numerical solutions for Newell–Whitehead–Segel partial differential equation, which are implicit exponential finite difference method and fully implicit exponential finite difference method. Implicit exponential methods… read more here.
Keywords: difference; difference methods; exponential finite; whitehead segel ... See more keywords
Moving boundary transformation for American call options with transaction cost: finite difference methods and computing
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DOI: 10.1080/00207160.2015.1108409
Abstract: ABSTRACT The pricing of American call option with transaction cost is a free boundary problem. Using a new transformation method the boundary is made to follow a certain known trajectory in time. The new transformed… read more here.
Keywords: finite difference; american call; transaction cost; difference methods ... See more keywords
A note on finite difference methods for nonlinear fractional differential equations with non-uniform meshes
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DOI: 10.1080/00207160.2017.1381691
Abstract: ABSTRACT We consider finite difference methods for solving nonlinear fractional differential equations in the Caputo fractional derivative sense with non-uniform meshes. Under the assumption that the Caputo derivative of the solution of the fractional differential… read more here.
Keywords: difference methods; uniform meshes; fractional differential; finite difference ... See more keywords
Two-Level Finite Difference Methods for Simulating the High-Dimensional Lagging Models of Heat Conduction
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DOI: 10.1080/01630563.2017.1287727
Abstract: ABSTRACT Heat transfer at microscale plays an important role in microtechnology applications. First, this paper is concerned with the numerical solution of a two-dimensional (2D) heat transfer equation at microscale through a second-order alternating direction… read more here.
Keywords: two level; adi method; difference methods; method ... See more keywords
Finite difference methods for 2D shallow water equations with dispersion
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DOI: 10.1515/rnam-2019-0009
Abstract: Abstract Basic properties of some finite difference schemes for two-dimensional nonlinear dispersive equations for hydrodynamics of surface waves are considered. It is shown that stability conditions for difference schemes of shallow water equations are qualitatively… read more here.
Keywords: difference; difference methods; water equations; finite difference ... See more keywords