One‐Dimensional Space‐Charge Theory. I. Generalization

1966 ◽  
Vol 37 (1) ◽  
pp. 437-438 ◽  
Author(s):  
Walton L. Howes
Keyword(s):  
Space Charge ◽  
Dimensional Space ◽  
One Dimensional

Parametric surfaces

1949 ◽  
Vol 45 (1) ◽  
pp. 14-23 ◽  
Author(s):  
A. S. Besicovitch
Keyword(s):  
Dimensional Space ◽  
Parametric Surfaces ◽  
Rectifiable Curve ◽  
One Dimensional ◽  
Dimensional Measure

In 1914 Carathéodory defined m–dimensional measure in n–dimensional space. He considered one-dimensional measure as a generalization of length and he proved that the length of a rectifiable curve coincides with its one-dimensional measure.

scholarly journals A new method for solving a class of heat conduction equations

2015 ◽  
Vol 19 (4) ◽  
pp. 1205-1210
Author(s):  
Yi Tian ◽  
Zai-Zai Yan ◽  
Zhi-Min Hong
Keyword(s):  
Monte Carlo ◽  
Heat Conduction ◽  
Dimensional Space ◽  
Variable Coefficients ◽  
Algebraic Equations ◽  
Governing Equations ◽  
One Dimensional ◽  
Sparse System ◽  
Linear Algebraic Equations ◽  
Crank Nicolson

A numerical method for solving a class of heat conduction equations with variable coefficients in one dimensional space is demonstrated. This method combines the Crank-Nicolson and Monte Carlo methods. Using Crank-Nicolson method, the governing equations are discretized into a large sparse system of linear algebraic equations, which are solved by Monte Carlo method. To illustrate the usefulness of this technique, we apply it to two problems. Numerical results show the performance of the present work.

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