Solving the Nonlinear Algebraic Equations with Monte Carlo Method

2000 ◽  
pp. 3-15
Author(s):  
S. Ermakov ◽  
I. Kaloshin
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Algebraic Equations ◽  
Nonlinear Algebraic Equations

Monte Carlo method for the real and complex fuzzy system of linear algebraic equations

2019 ◽  
Vol 24 (2) ◽  
pp. 1255-1270
Author(s):  
Behrouz Fathi-Vajargah ◽  
Zeinab Hassanzadeh
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Fuzzy System ◽  
Algebraic Equations ◽  
The Real ◽  
Linear Algebraic Equations

scholarly journals Monte Carlo method for solving a parabolic problem

2016 ◽  
Vol 20 (3) ◽  
pp. 933-937
Author(s):  
Yi Tian ◽  
Zai-Zai Yan
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Random Sampling ◽  
Parabolic Problem ◽  
Test Problems ◽  
Algebraic Equations ◽  
Governing Equations ◽  
Sparse System ◽  
Linear Algebraic Equations ◽  
Crank Nicolson

In this paper, we present a numerical method based on random sampling for a parabolic problem. This method combines use of the Crank-Nicolson method and Monte Carlo method. In the numerical algorithm, we first discretize governing equations by Crank-Nicolson method, and obtain a large sparse system of linear algebraic equations, then use Monte Carlo method to solve the linear algebraic equations. To illustrate the usefulness of this technique, we apply it to some test problems.

scholarly journals A new Walk on Equations Monte Carlo method for solving systems of linear algebraic equations

2015 ◽  
Vol 39 (15) ◽  
pp. 4494-4510 ◽  
Author(s):  
Ivan Dimov ◽  
Sylvain Maire ◽  
Jean Michel Sellier
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Algebraic Equations ◽  
Linear Algebraic Equations

Outbursts of comet Schwassmann-Wachmann 1, and the cloud of interplanetary boulders

1974 ◽  
Vol 22 ◽  
pp. 307 ◽  
Author(s):  
Zdenek Sekanina
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Interplanetary Space ◽  
Porous Matrix ◽  
Maximum Diameter ◽  
Expansion Velocity ◽  
Solid Constituent ◽  
Meteoric Material ◽  
Periodic Comet

AbstractIt is suggested that the outbursts of Periodic Comet Schwassmann-Wachmann 1 are triggered by impacts of interplanetary boulders on the surface of the comet’s nucleus. The existence of a cloud of such boulders in interplanetary space was predicted by Harwit (1967). We have used the hypothesis to calculate the characteristics of the outbursts – such as their mean rate, optically important dimensions of ejected debris, expansion velocity of the ejecta, maximum diameter of the expanding cloud before it fades out, and the magnitude of the accompanying orbital impulse – and found them reasonably consistent with observations, if the solid constituent of the comet is assumed in the form of a porous matrix of lowstrength meteoric material. A Monte Carlo method was applied to simulate the distributions of impacts, their directions and impact velocities.

Structures and crystallization of vacuum-deposited amorphous Se and Sb films

1990 ◽  
Vol 48 (4) ◽  
pp. 140-141
Author(s):  
Makoto Shiojiri ◽  
Toshiyuki Isshiki ◽  
Tetsuya Fudaba ◽  
Yoshihiro Hirota
Keyword(s):  
Monte Carlo ◽  
Electron Microscope ◽  
Monte Carlo Method ◽  
Computer Program ◽  
Radial Distribution ◽  
Film Formation ◽  
Amorphous State ◽  
Two Dimensional ◽  
Amorphous Films ◽  
Binding Condition

In hexagonal Se crystal each atom is covalently bound to two others to form an endless spiral chain, and in Sb crystal each atom to three others to form an extended puckered sheet. Such chains and sheets may be regarded as one- and two- dimensional molecules, respectively. In this paper we investigate the structures in amorphous state of these elements and the crystallization.HRTEM and ED images of vacuum-deposited amorphous Se and Sb films were taken with a JEM-200CX electron microscope (Cs=1.2 mm). The structure models of amorphous films were constructed on a computer by Monte Carlo method. Generated atoms were subsequently deposited on a space of 2 nm×2 nm as they fulfiled the binding condition, to form a film 5 nm thick (Fig. 1a-1c). An improvement on a previous computer program has been made as to realize the actual film formation. Radial distribution fuction (RDF) curves, ED intensities and HRTEM images for the constructed structure models were calculated, and compared with the observed ones.

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