Accurate Computation of Mathieu Functions

2013 ◽  
Vol 8 (2) ◽  
pp. 1-133 ◽  
Author(s):  
Malcolm M. Bibby ◽  
Andrew F. Peterson
Keyword(s):  
Mathieu Functions ◽  
Accurate Computation

A Fast Volume Integral Equation Solver with Linear Basis Functions for the Accurate Computation of EM Fields in MRI

2020 ◽  
pp. 1-1
Author(s):  
Ioannis P. Georgakis ◽  
Ilias I. Giannakopoulos ◽  
Mikhail S. Litsarev ◽  
Athanasios G. Polimeridis
Keyword(s):  
Integral Equation ◽  
Basis Functions ◽  
Volume Integral ◽  
Volume Integral Equation ◽  
Linear Basis ◽  
Accurate Computation

scholarly journals Transient Pressure-Driven Electroosmotic Flow through Elliptic Cross-Sectional Microchannels with Various Eccentricities

Computation ◽  
2021 ◽  
Vol 9 (3) ◽  
pp. 27
Author(s):  
Nattakarn Numpanviwat ◽  
Pearanat Chuchard
Keyword(s):  
Laplace Transform ◽  
Electroosmotic Flow ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Mathieu Functions ◽  
Navier Stokes Equations ◽  
Flow Rates ◽  
Elliptic Cross ◽  
Flow Through ◽  
Relative Errors

The semi-analytical solution for transient electroosmotic flow through elliptic cylindrical microchannels is derived from the Navier-Stokes equations using the Laplace transform. The electroosmotic force expressed by the linearized Poisson-Boltzmann equation is considered the external force in the Navier-Stokes equations. The velocity field solution is obtained in the form of the Mathieu and modified Mathieu functions and it is capable of describing the flow behavior in the system when the boundary condition is either constant or varied. The fluid velocity is calculated numerically using the inverse Laplace transform in order to describe the transient behavior. Moreover, the flow rates and the relative errors on the flow rates are presented to investigate the effect of eccentricity of the elliptic cross-section. The investigation shows that, when the area of the channel cross-sections is fixed, the relative errors are less than 1% if the eccentricity is not greater than 0.5. As a result, an elliptic channel with the eccentricity not greater than 0.5 can be assumed to be circular when the solution is written in the form of trigonometric functions in order to avoid the difficulty in computing the Mathieu and modified Mathieu functions.

Potential and matrix elements of the hamiltonian of internal rotation in molecules in the basis set of Mathieu functions

2015 ◽  
Vol 119 (2) ◽  
pp. 191-194 ◽  
Author(s):  
V. V. Turovtsev ◽  
Yu. D. Orlov ◽  
A. N. Tsirulev
Keyword(s):  
Internal Rotation ◽  
Basis Set ◽  
Matrix Elements ◽  
Mathieu Functions

Accurate Computation of Gaussian Quadrature for Tension Powers

2007 ◽  
Author(s):  
Saša Singer ◽  
Theodore E. Simos ◽  
George Psihoyios ◽  
Ch. Tsitouras
Keyword(s):  
Gaussian Quadrature ◽  
Accurate Computation

scholarly journals On the Computation of Mathieu Functions

1946 ◽  
Vol 25 (1-4) ◽  
pp. 1-20 ◽  
Author(s):  
Gertrude Blanch
Keyword(s):  
Mathieu Functions

Fast and accurate computation of Bessel functions with (large) complex order and argument

2009 ◽  
Vol 207 (2) ◽  
pp. 442-447 ◽  
Author(s):  
R.W. Smink ◽  
B.P. de Hon ◽  
A.G. Tijhuis
Keyword(s):  
Bessel Functions ◽  
Complex Order ◽  
Large Complex ◽  
Accurate Computation

scholarly journals Chemical-shift tensors of heavy nuclei in network solids: a DFT/ZORA investigation of 207Pb chemical-shift tensors using the bond-valence method

2015 ◽  
Vol 17 (38) ◽  
pp. 25014-25026 ◽  
Author(s):  
Fahri Alkan ◽  
C. Dybowski
Keyword(s):  
Chemical Shift ◽  
Quantum Chemistry ◽  
Principal Components ◽  
Bond Valence ◽  
Cluster Models ◽  
Magnetic Shielding ◽  
Heavy Nuclei ◽  
Chemical Shift Tensors ◽  
Accurate Computation ◽  
Bond Valence Model

Accurate computation of 207Pb magnetic shielding principal components is within the reach of quantum chemistry methods by employing relativistic ZORA/DFT and cluster models adapted from the bond valence model.

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