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Numerical Solution of Nonlinear Equations
ACM Transactions on Mathematical Software, 1979The numermal solutmn of n nonhnear equatmns in n varmbles using the methods of Newton, Brown, and Brent is drscussed. The algorithms are described in detail and their lmplementatmns are compared on a set of test problems.
More, Jorge J., Cosnard, Michel Y.
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Numerical Solutions in Remote Sensing
Applied Optics, 1975Several aspects of the behavior of Fredholm integral equations are examined in this paper. It is shown that collocation methods are better in general than least squares methods in linear approaches. The amplification of random noise inherent to the numerical inversion of the equation puts an upper limit to the information content of an ill-conditioned ...
J Y, Wang, R, Goulard
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Numerical solution of Burger's equation
Communications in Numerical Methods in Engineering, 1993AbstractIn the present paper numerical solutions of the one‐dimensional Burger equation are obtained. The technique of finitely reproducing non‐linearities introduced by Bazley is used. This technique when applied to Burger's equation gives a method where a system of non‐linear ordinary differential equations is to be solved.
Mittal, R. C., Singhal, Poonam
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2013
The peridynamic (PD) equation of motion is an integro-differential equation, which is not usually amenable for analytical solutions. Therefore, its solution is constructed by using numerical techniques for spatial and time integrations. The spatial integration can be performed by using the collocation method of a meshless scheme due to its simplicity ...
Erdogan Madenci, Erkan Oterkus
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The peridynamic (PD) equation of motion is an integro-differential equation, which is not usually amenable for analytical solutions. Therefore, its solution is constructed by using numerical techniques for spatial and time integrations. The spatial integration can be performed by using the collocation method of a meshless scheme due to its simplicity ...
Erdogan Madenci, Erkan Oterkus
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2009
To learn about the causes of aggregate fluctuations is one of the basic goals of Macroeconomics. One of the main characteristics of aggregate fluctuations is that business cycles are neither regular nor predictable. Because of that, most economists consider that there are different shocks impinging on the economy, which are different in nature and ...
Alfonso Novales +2 more
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To learn about the causes of aggregate fluctuations is one of the basic goals of Macroeconomics. One of the main characteristics of aggregate fluctuations is that business cycles are neither regular nor predictable. Because of that, most economists consider that there are different shocks impinging on the economy, which are different in nature and ...
Alfonso Novales +2 more
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2014
In order to obtain solutions of the integral equations arising in electroanalytical chemistry, numerical methods are often necessary. Such methods are usually based on the general idea of replacing integrals by finite sums. The methods for one-dimensional integral equations can be divided into quadrature methods, product integration methods, and ...
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In order to obtain solutions of the integral equations arising in electroanalytical chemistry, numerical methods are often necessary. Such methods are usually based on the general idea of replacing integrals by finite sums. The methods for one-dimensional integral equations can be divided into quadrature methods, product integration methods, and ...
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1993
Abstract There are several types of difficulties in finding a solution to the general contact-impact problem formulated in the preceding chapter. The difficulties come from the inherent non-linearity of the contact-impact problem itself and other possible non-linearities. First of all, the equilibrium (or fictitious ‘dynamic equilibrium’)
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Abstract There are several types of difficulties in finding a solution to the general contact-impact problem formulated in the preceding chapter. The difficulties come from the inherent non-linearity of the contact-impact problem itself and other possible non-linearities. First of all, the equilibrium (or fictitious ‘dynamic equilibrium’)
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2008
In this chapter several numerical methods frequently employed in reactor engineering are introduced. To simulate the important phenomena determining single- and multiphase reactive flows, mathematical equations with different characteristics have to be solved. The relevant equations considered are the governing equations of single phase fluid mechanics,
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In this chapter several numerical methods frequently employed in reactor engineering are introduced. To simulate the important phenomena determining single- and multiphase reactive flows, mathematical equations with different characteristics have to be solved. The relevant equations considered are the governing equations of single phase fluid mechanics,
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2012
Introduction We have seen that when the equations of motion of an offshore facility can be modeled as linear, there are sometimes analytical methods available that allow us to calculate the statistical properties of the response. In general, this possibility is lost as soon as nonlinear elements enter the dynamic model.
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Introduction We have seen that when the equations of motion of an offshore facility can be modeled as linear, there are sometimes analytical methods available that allow us to calculate the statistical properties of the response. In general, this possibility is lost as soon as nonlinear elements enter the dynamic model.
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