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The Finite Difference Method
This chapter introduces the finite difference method and develops finite difference solutions for the advection dispersion equation and a non-linear...
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Finite difference based stress integration algorithm for crystal plasticity finite element method
In this study, we present a Finite Difference Method (FDM)-based stress integration algorithm for Crystal Plasticity Finite Element Method (CPFEM)....
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Adaptive Dynamic Grids and Mimetic Finite Difference Method for Miscible Displacement Problem
AbstractWe consider the solution of a two-phase miscible displacement problem on dynamic adaptive meshes using the mimetic finite difference method....
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A novel high accuracy finite-difference time-domain method
The finite-difference time-domain (FDTD) method is widely used for numerical simulations of electromagnetic waves and acoustic waves. It is known,...
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A Nonstandard Finite Difference Method for a General Epidemic Model
This paper aims to investigate the qualitative properties of a general SIR model. The model includes a general function that describes the effect...
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A simplified calculation for adaptive coefficients of finite-difference frequency-domain method
The finite-difference frequency domain (FDFD) method is widely applied for simulating seismic wavefields, and a key to achieving successful FDFD...
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Numerical Calculation of Energy Spectrum of Parabolic Quantum Well of Finite Depth Using Finite Difference Method
In this chapter, energy spectrum of parabolic Quantum Well of finite depth is numerically calculated and depicted graphically as well as using...
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Solving singularly perturbed fredholm integro-differential equation using exact finite difference method
ObjectivesIn this paper, a numerical scheme is designed for solving singularly perturbed Fredholm integro-differential equation. The scheme is...
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A Mimetic Finite-Difference Method for Two-Dimensional DC Resistivity Modeling
Nondestructive imaging and monitoring of the earth’s subsurface using the geoelectric method require reliable and versatile numerical techniques for...
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Uniform convergence analysis of a new adaptive upwind finite difference method for singularly perturbed convection-reaction-diffusion boundary value problems
In this paper, a new adaptive upwind finite difference method based on the arc-length equidistribution principle is studied for solving the general...
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A Novel Decomposition as a Fast Finite Difference Method for Second Derivatives
In this paper, we propose a fast solver for the linear system-induced from applying the finite difference method. For this purpose, we provide a new...
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Source Identification for Parabolic Equations from Integral Observations by the Finite Difference Splitting Method
We study the problem of reconstructing an unknown source term in parabolic equations from integral observations. It is reformulated into a...
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Numerical modelling of groundwater radionuclide transport with finite difference-based method of lines
In this study, the advection–dispersion equation with decay is numerically solved by the finite difference-based method of lines (FD-MOL) to simulate...
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A fast finite difference method for 2D time variable fractional mobile/immobile equation
In this paper, we establish a fast Crank–Nicolson L1 finite difference scheme for two-dimensional time variable fractional mobile/immobile diffusion...
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Error bounds for a least squares meshless finite difference method on closed manifolds
We present an error bound for a least squares version of the kernel based meshless finite difference method for elliptic differential equations on...
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On the finite difference method with penalty for numerical solution of PDEs over curved domains
This paper aims to decipher the elliptic PDEs defined over curved complex domains with a penalty approach in a finite difference scheme. Using the...
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2D Laplace-Fourier domain acoustic wave equation modeling with an optimal finite-difference method
Laplace-Fourier (L-F) domain finite-difference (FD) forward modeling is an important foundation for L-F domain full-waveform inversion (FWI). An...
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Numerical Solution of Nonlinear Reaction-Advection-Diffusion Equation in Sense of Caputo-Fabrizio Derivative with Finite Difference and Collocation Method
In this paper, we consider a nonlinear reaction-diffusion equation with a Caputo-Fabrizio derivative and its solution is obtained by the finite...
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A Hybrid Spectral-Finite Difference Method for Numerical Pricing of Time-Fractional Black–Scholes Equation
In this paper, option pricing through introducing a novel hybrid method for solving time-fractional Black–Scholes equation is considered. The...
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Numerical Modeling of Skin Bioheat Transfer Using Finite Difference Method
Skin bioheat transfer is heat transfer in the cross-section of the skin tissue. Pennes bioheat transfer equation is the basis of skin bioheat...