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Numerical Solution of Linear IntegroDifferential Equations
, 2008
"... Problem Statement: Integrodifferential equations find special applicability within scientific and mathematical disciplines. In this study, an analytical scheme for solving Integrodifferential equations was presented. Approach: We employed the Homotopy Analysis Method (HAM) to solve linear Fredholm ..."
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Cited by 1 (0 self)
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Fredholm integrodifferential equations. Results: Error analysis and illustrative examples were included to demonstrate the validity and applicability of the technique. MATLAB 7 was used to carry out the computations. Conclusion/Recommendations: From now we can use HAM as a novel solver for linear Integrodifferential
Parabolic IntegroDifferential Equations
"... In this article, a priori error analysis is discussed for an hplocal discontinuous Galerkin (LDG) approximation to a parabolic integrodifferential equation. It is shown that the L 2norm of the gradient and the L 2norm of the potential are optimal in the discretizing parameter h and suboptimal in ..."
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In this article, a priori error analysis is discussed for an hplocal discontinuous Galerkin (LDG) approximation to a parabolic integrodifferential equation. It is shown that the L 2norm of the gradient and the L 2norm of the potential are optimal in the discretizing parameter h and suboptimal
For Most Large Underdetermined Systems of Linear Equations the Minimal ℓ1norm Solution is also the Sparsest Solution
 Comm. Pure Appl. Math
, 2004
"... We consider linear equations y = Φα where y is a given vector in R n, Φ is a given n by m matrix with n < m ≤ An, and we wish to solve for α ∈ R m. We suppose that the columns of Φ are normalized to unit ℓ 2 norm 1 and we place uniform measure on such Φ. We prove the existence of ρ = ρ(A) so that ..."
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Cited by 560 (10 self)
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We consider linear equations y = Φα where y is a given vector in R n, Φ is a given n by m matrix with n < m ≤ An, and we wish to solve for α ∈ R m. We suppose that the columns of Φ are normalized to unit ℓ 2 norm 1 and we place uniform measure on such Φ. We prove the existence of ρ = ρ(A) so
Sequential data assimilation with a nonlinear quasigeostrophic model using Monte Carlo methods to forecast error statistics
 J. Geophys. Res
, 1994
"... . A new sequential data assimilation method is discussed. It is based on forecasting the error statistics using Monte Carlo methods, a better alternative than solving the traditional and computationally extremely demanding approximate error covariance equation used in the extended Kalman filter. The ..."
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Cited by 782 (22 self)
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. A new sequential data assimilation method is discussed. It is based on forecasting the error statistics using Monte Carlo methods, a better alternative than solving the traditional and computationally extremely demanding approximate error covariance equation used in the extended Kalman filter
Gravity with Gravitas: a Solution to the Border Puzzle
, 2001
"... Gravity equations have been widely used to infer trade ow effects of various institutional arrangements. We show that estimated gravity equations do not have a theoretical foundation. This implies both that estimation suffers from omitted variables bias and that comparative statics analysis is unfo ..."
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Cited by 610 (3 self)
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is unfounded. We develop a method that (i) consistently and ef ciently estimates a theoretical gravity equation and (ii) correctly calculates the comparative statics of trade frictions. We apply the method to solve the famous McCallum border puzzle. Applying our method, we nd that national borders reduce
Numerical solution of the linear FredholmVolterra IntegroDifferential equations by the Tau method with an error
"... The Tau method, produces approximate polynomial solutions of differential, integral and integrodifferential equations. in this paper extension of the Tau method has been done for the numerical solution of the general form of linear FredholmVolterra IntegroDifferential equations. An efficient erro ..."
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error estimation for the Tau method is also introduced. Details of the method are presented and some numerical results along with estimated errors are given to clarify the method and its error estimator. keywords:Tau method; Fredholm and Volterra integral and IntegroDifferential equations 1 1
Numerical Solutions of the Euler Equations by Finite Volume Methods Using RungeKutta TimeStepping Schemes
, 1981
"... A new combination of a finite volume discretization in conjunction with carefully designed dissipative terms of third order, and a Runge Kutta time stepping scheme, is shown to yield an effective method for solving the Euler equations in arbitrary geometric domains. The method has been used to deter ..."
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Cited by 456 (78 self)
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A new combination of a finite volume discretization in conjunction with carefully designed dissipative terms of third order, and a Runge Kutta time stepping scheme, is shown to yield an effective method for solving the Euler equations in arbitrary geometric domains. The method has been used
Results 1  10
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779,225