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1986
Consider the problem $$\frac{{{\text{d}}y}}{{{\text{d}}x}} = 0$$ where y = a when x ...
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Consider the problem $$\frac{{{\text{d}}y}}{{{\text{d}}x}} = 0$$ where y = a when x ...
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Finite-difference and finite-element methods of approximation [PDF]
Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences, 1971 The finite-difference and finite-element methods for approximating the solution of elliptic boundary-value problems are discussed. The analysis of the order of accuracy is outlined, and the results compared, with some comment on special problems connected with singularities.
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Finite-difference time-domain methods
Nature Reviews Methods Primers, 2023F. L. Teixeira +9 more
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The Method of Finite Differences
1985This method of investigating various problems for differential equations consists of reducing them to systems of algebraic equations in which the unknowns are the values of grid functions u Δ at the vertices of the grids ΩΔ, and then examining the limit process when the lengths of the sides of the cells in the grid tend to zero.
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2018
This chapter will introduce one of the most straightforward numerical simulation methods: the finite difference method. We will show how to approximate derivatives using finite differences and discretize the equation and computational domain based on that. The discretization will be discussed for spatial and temporal derivatives sequentially.
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This chapter will introduce one of the most straightforward numerical simulation methods: the finite difference method. We will show how to approximate derivatives using finite differences and discretize the equation and computational domain based on that. The discretization will be discussed for spatial and temporal derivatives sequentially.
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Finite Difference and Finite Element Methods
1999Applications of the finite difference and finite element techniques to vibroacoustic problems are presented. The basic ideas and the mathematical descriptions are outlined for both of the methods and examples are given to demonstrate the potential of such numerical techniques.
Tonni F. Johansen +2 more
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P-SV wave propagation in heterogeneous media: Velocity‐stress finite‐difference method
, 1986J. Virieux
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2010
The finite-difference method can be considered the classical and most frequently applied method for the numerical simulation of seismic wave propagation. It is based on the approximation of an exact derivative ∂x f (x i) at a grid position x i in terms of the function f evaluated at a finite number of neighbouring grid points.
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The finite-difference method can be considered the classical and most frequently applied method for the numerical simulation of seismic wave propagation. It is based on the approximation of an exact derivative ∂x f (x i) at a grid position x i in terms of the function f evaluated at a finite number of neighbouring grid points.
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Finite difference and finite element methods
Computer Physics Communications, 1976Abstract The relationships between and relative advantages of finite difference and finite element methods are discussed. The less familiar finite element methods are described first for equilibrium problems: it is shown how quadratic elements on right triangles lead to natural generalisations of the powerful, fourth order accurate nine-point ...
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