Numerical solution of fractional Black‐Scholes model of American put option pricing via a nonstandard finite difference method: Stability and convergent analysis
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DOI: 10.1002/mma.5913
Abstract: In this paper, a free boundary fractional Black‐Scholes (FBS) model of American put option pricing is investigated. To convert the free boundary FBS model to a model with known boundary condition, the quasi‐stationary method is… read more here.
Keywords: put option; nonstandard finite; american put; finite difference ... See more keywords
Finite difference scheme for time‐space fractional diffusion equation with fractional boundary conditions
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DOI: 10.1002/mma.6132
Abstract: In this paper, the finite difference scheme is developed for the time‐space fractional diffusion equation with Dirichlet and fractional boundary conditions. The time and space fractional derivatives are considered in the senses of Caputo and… read more here.
Keywords: time space; space fractional; scheme; finite difference ... See more keywords
Conservative finite‐difference scheme for computer simulation of contrast 3D spatial‐temporal structures induced by a laser pulse in a semiconductor
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DOI: 10.1002/mma.6245
Abstract: The numerical approach for computer simulation of femtosecond laser pulse interaction with a semiconductor is considered under the formation of 3D contrast time‐dependent spatiotemporal structures. The problem is governed by the set of nonlinear partial… read more here.
Keywords: computer simulation; difference; laser pulse; finite difference ... See more keywords
Nonstandard finite difference schemes for general linear delay differential systems
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DOI: 10.1002/mma.7002
Abstract: This paper deals with the construction of non‐standard finite difference methods for coupled linear delay differential systems in the general case of non‐commuting matrix coefficients. Based on an expression for the exact solution of the… read more here.
Keywords: finite difference; delay differential; linear delay; differential systems ... See more keywords
A Damped Dynamic Finite Difference Approach for Modeling Static Stress–Strain Fields
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DOI: 10.1007/s00024-019-02207-2
Abstract: Modeling dynamic and static responses of an elastic medium often employs different numerical schemes. By introducing damping into the system, we show how the widely used time-marching staggered finite difference (FD) approach in solving elastodynamic… read more here.
Keywords: strain fields; model; difference approach; approach ... See more keywords
Unconditional $$L^{\infty }$$L∞-convergence of two compact conservative finite difference schemes for the nonlinear Schrödinger equation in multi-dimensions
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DOI: 10.1007/s10092-018-0277-0
Abstract: This paper is concerned with the unconditional and optimal $$L^{\infty }$$L∞-error estimates of two fourth-order (in space) compact conservative finite difference time domain schemes for solving the nonlinear Schrödinger equation in two or three space… read more here.
Keywords: difference; nonlinear schr; schr dinger; finite difference ... See more keywords
On a high-order Gaussian radial basis function generated Hermite finite difference method and its application
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DOI: 10.1007/s10092-021-00443-4
Abstract: Recently, several improvements over the radial basis function generated finite difference method have been appeared numerically and theoretically in literature. Suitable convergence orders can be obtained once they are combined with stable evaluation schemes. However,… read more here.
Keywords: radial basis; finite difference; function; function generated ... See more keywords
Propagation of One- and Two-Dimensional Discrete Waves Under Finite Difference Approximation
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DOI: 10.1007/s10208-020-09445-0
Abstract: We analyze the propagation properties of the numerical versions of one- and two-dimensional wave equations, semi-discretized in space by finite difference schemes. We focus on high-frequency solutions whose propagation can be described, both at the… read more here.
Keywords: propagation; one two; high frequency; two dimensional ... See more keywords
A conservative compact finite difference scheme for the coupled Schrödinger-KdV equations
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DOI: 10.1007/s10444-020-09758-2
Abstract: In this paper, a conservative compact finite difference scheme is presented to numerically solve the coupled Schrödinger-KdV equations. The analytic solutions of the coupled equations have some invariants such as the number of plasmons, the… read more here.
Keywords: conservative compact; scheme; difference scheme; compact finite ... See more keywords
A finite difference pair with improved phase and stability properties
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DOI: 10.1007/s10910-017-0787-z
Abstract: A new finite difference pair is produced in this paper, for the first time in the literature. The characteristics of the new finite diffence pair are: (1) is of symmetric two-step, (2) is four-stages, (3)… read more here.
Keywords: finite difference; pair; difference pair; stability properties ... See more keywords
A hybrid finite difference pair with maximum phase and stability properties
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DOI: 10.1007/s10910-017-0793-1
Abstract: We develop, in the present paper and for the first time in the literature, a new hybrid finite difference pair of symmetric two-step. The basic properties of the new pair are:is of symmetric form,is of… read more here.
Keywords: pair; hybrid finite; difference pair; layer approximation ... See more keywords