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ON CERTAIN FINITEDIFFERENCE METHODS
"... Two finitedifference methods for, geophysical.fluid problems are described, and stability conditions of these schemes arc discussed. These two schemes are formulated based upon a similar procedure given by Lax and Wendroff in order to obtain a secondorder accuracy in finitedifference equations. H ..."
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Two finitedifference methods for, geophysical.fluid problems are described, and stability conditions of these schemes arc discussed. These two schemes are formulated based upon a similar procedure given by Lax and Wendroff in order to obtain a secondorder accuracy in finitedifference equations
FINITE DIFFERENCE METHOD ON TRIANGULATION
"... In this paper, we present a new method for solving Partial Differential Equations (PDE). This method combines the use of features of both Finite Element Methods (FEM) and Finite Difference methods (FDM). Similar to the FEM, this method uses the triangulation technique and function approximation. Mor ..."
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In this paper, we present a new method for solving Partial Differential Equations (PDE). This method combines the use of features of both Finite Element Methods (FEM) and Finite Difference methods (FDM). Similar to the FEM, this method uses the triangulation technique and function approximation
Fairing by Finite Difference Methods
 Schumaker: Mathematical Methods for Curves and Surfaces II, Vanderbilt
, 1998
"... . We propose an efficient and flexible scheme to fairly interpolate or approximate the vertices of a given triangular mesh. Instead of generating a piecewise polynomial representation, our output will be a refined mesh with vertices lying densely on a surface with minimum bending energy. To obtain t ..."
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Cited by 4 (0 self)
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those, we generalize the finite differences technique to parametric meshes. The use of local parameterizations (charts) makes it possible to cast the minimization of nonlinear geometric functionals into solving a sparse linear system. Efficient multigrid solvers can be applied which leads to fast
C. Finite Difference Methods
"... The earth, the moon and the sun are the celestial bodies to he considered in studying the tides, since the other ones have a negligible influence. Indeed, the tide generating forces exerted on the earth by a celestial body are (obviously) proportional to its mass and (reasonably) to the cubic invers ..."
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by the moon (or the sun). Consider the place where the moon is seen on the zenith (the closest one), then the one seen on the nadir (the farthest), then any intermediate one. Due to the different distance from the moon,.there will be an obvious increase of gravitational attraction when moving from
On the waveletoptimized finite difference method
 ICASE REPORT, (949, NASA CR191601
, 1994
"... When one considers the effect in the physical space, Daubechiesbased wavelet methods are equivalent to finite difference methods with grid refinement in regions of the domain where small scale structure exists. Adding a wavelet basis function at a given scale and location where one has a correspond ..."
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Cited by 11 (2 self)
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When one considers the effect in the physical space, Daubechiesbased wavelet methods are equivalent to finite difference methods with grid refinement in regions of the domain where small scale structure exists. Adding a wavelet basis function at a given scale and location where one has a
FINITEDIFFERENCE METHOD FOR PARAMETERIZED SINGULARLY PERTURBED PROBLEM
, 2004
"... We study uniform finitedifference method for solving firstorder singularly perturbed boundary value problem (BVP) depending on a parameter. Uniform error estimates in the discrete maximum norm are obtained for the numerical solution. Numerical results support the theoretical analysis. 1. ..."
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We study uniform finitedifference method for solving firstorder singularly perturbed boundary value problem (BVP) depending on a parameter. Uniform error estimates in the discrete maximum norm are obtained for the numerical solution. Numerical results support the theoretical analysis. 1.
A finitedifference method for the valuation of variance swaps
 Journal of Computational Finance
, 2001
"... We develop here a finitedifference approach for valuing a discretely sampled variance swap within an extended Black–Scholes framework. This approach incorporates the observed volatility skew and is capable of handling various definitions of the variance. It is benchmarked against Monte Carlo simula ..."
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Cited by 5 (0 self)
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simulation in the presence of a volatility skew and is shown to provide extremely accurate values for a variance swap. Our method is based on decomposing the problem of valuing a variance swap into a set of onedimensional PDE problems, each of which is then solved using a finitedifference method. 1.
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