Improper Integrals

1994 ◽  
pp. 62-67
Author(s):  
Robert J. Lopez
Keyword(s):  
Improper Integrals

scholarly journals Improving CAS capabilities: New rules for computing improper integrals

2018 ◽  
Vol 316 ◽  
pp. 525-540 ◽  
Author(s):  
José L. Galán-García ◽  
Gabriel Aguilera-Venegas ◽  
María Á. Galán-García ◽  
Pedro Rodríguez-Cielos ◽  
Iván Atencia-Mc.Killop
Keyword(s):  
Improper Integrals

Fast and high-precision calculation of earth return mutual impedance between conductors over a multilayered soil

2018 ◽  
Vol 37 (3) ◽  
pp. 1214-1227 ◽  
Author(s):  
Junjie Ma
Keyword(s):  
Quadrature Rule ◽  
Content Type ◽  
Mutual Impedance ◽  
Numerical Tests ◽  
Sommerfeld Integral ◽  
The Earth ◽  
Finite Integral ◽  
Infinite Integral ◽  
Improper Integrals ◽  
Differential Matrix

Purpose Solutions for the earth return mutual impedance play an important role in analyzing couplings of multi-conductor systems. Generally, the mutual impedance is approximated by Pollaczek integrals. The purpose of this paper is devising fast algorithms for calculation of this kind of improper integrals and its applications. Design/methodology/approach According to singular points, the Pollaczek integral is divided into two parts: the finite integral and the infinite integral. The finite part is computed by combining an efficient Levin method, which is implemented with a Chebyshev differential matrix. By transforming the integration path, the tail integral is calculated with help of a transformed Clenshaw–Curtis quadrature rule. Findings Numerical tests show that this new method is robust to high oscillation and nearly singularities. Thus, it is suitable for evaluating Pollaczek integrals. Furthermore, compared with existing method, the presented algorithm gives high-order approaches for the earth return mutual impedance between conductors over a multilayered soil with wide ranges of parameters. Originality/value An efficient truncation strategy is proposed to accelerate numerical calculation of Pollaczek integral. Compared with existing algorithms, this method is easier to be applied to computation of similar improper integrals, such as Sommerfeld integral.

scholarly journals Numerical quadrature of some improper integrals

1954 ◽  
Vol 12 (2) ◽  
pp. 188-194 ◽  
Author(s):  
H. Serbin
Keyword(s):  
Numerical Quadrature ◽  
Improper Integrals

FEM-simulation of superconducting linear acceleration system for pellet injection

2020 ◽  
Vol 64 (1-4) ◽  
pp. 1469-1475
Author(s):  
Teruou Takayama ◽  
Takazumi Yamaguchi ◽  
Ayumu Saitoh ◽  
Atsushi Kamitani
Keyword(s):  
Magnetic Field ◽  
High Temperature ◽  
Applied Magnetic Field ◽  
Integration Method ◽  
Fem Simulation ◽  
Linear Acceleration ◽  
Regularization Technique ◽  
Acceleration Time ◽  
Pellet Injection ◽  
Improper Integrals

In order to simulate the high-temperature superconducting (HTS) linear acceleration (SLA) system for the pellet injection, the integration method of the applied magnetic field generated from the acceleration coil has been proposed. To this end, the regularization technique is used in the evaluation of the improper integrals, and simultaneously, a FEM code is developed for analyzing the shielding current density in an HTS film. In addition, the SLA system has been simulated using the code. The results of the computations show that the accuracy of the applied magnetic field is considerably improved. In this sense, the regularization technique is a useful tool. Also by locating the outer coil, the acceleration time during which the pellet speed reaches 5 km/s is about 3.5 times shorter than that of the only use of the inner coil. These results mean that the outer coil is effective in the improvement of the acceleration performance for the SLA system.

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