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Numerical Solution of Variable-Order Fractional Differential Equations Using Bernoulli Polynomials

Somayeh Nemati, Pedro M. Lima, Delfim F. M. Torres
2021 Fractal and Fractional  
We introduce a new numerical method, based on Bernoulli polynomials, for solving multiterm variable-order fractional differential equations.  ...  An operational matrix of variable-order fractional integration was introduced for the Bernoulli functions.  ...  Numerical solution of multiterm variable-order fractional differential equations via shifted Legendre polynomials. Math. Meth. Appl.  ... 
doi:10.3390/fractalfract5040219 fatcat:rwjar2ntk5fkpe5wg3r3hkzgqy

Fourier's Method of Linear Programming and Its Dual

H. P. Williams
1986 The American mathematical monthly  
Theoretical approximation of solutions {For numerical analysis, see 65Rxx} 45L05 Theoretical approximation of solutions {For numerical analysis, see 65Rxx} 45L99 None of the above, but in this  ...  [See also 68M11] 68U99 None of the above, but in this section 68Wxx Algorithms {For numerical algorithms, see 65-XX; for combinatorics and graph theory, see 05C85, 68Rxx} 68W01 General 68W05 Nonnumerical  ...  motions 83C45 Quantization of the gravitational field 83C47 Methods of quantum field theory [See also 81T20] 83C50 Electromagnetic fields 83C55 Macroscopic interaction of the gravitational field with  ... 
doi:10.2307/2322281 fatcat:yvhgyh2epbcwdoqdhuaopkcrue

Acoustical measurements on stages of nine U.S. concert halls

A. C. Gade, John S. Bradley
1993 Journal of the Acoustical Society of America  
This paper will compare the results of room average data and several specific seat locations obtained from the two measurement systems with an analysis of the similarities and differences that arose.  ...  By 1980 the understanding of acoustics for concert halls had reached an interesting stage.  ...  Here, both piezos are considered perfectly bonded to the beam and the Bernoulli-Euler hypothesis is used for the displacement field.  ... 
doi:10.1121/1.406640 fatcat:omothtjqojcofd5ypx2oubadsy

Effects of measurement procedure and equipment on average room acoustic measurements

A. C. Gade, John S. Bradley, Gary W. Siebein
1993 Journal of the Acoustical Society of America  
This paper will compare the results of room average data and several specific seat locations obtained from the two measurement systems with an analysis of the similarities and differences that arose.  ...  By 1980 the understanding of acoustics for concert halls had reached an interesting stage.  ...  Here, both piezos are considered perfectly bonded to the beam and the Bernoulli-Euler hypothesis is used for the displacement field.  ... 
doi:10.1121/1.406634 fatcat:rah72seo75gtpgirf4x2ngcg24

Statistical relations among architectural features and objective acoustical measurements of concert halls

Gary W. Siebein, Wei‐hwa Chiang, Gary S. Madaras, Harold W. Doddington, Wilhelm K. Schwab, John S. Bradley, A. C. Gade
1993 Journal of the Acoustical Society of America  
This paper will compare the results of room average data and several specific seat locations obtained from the two measurement systems with an analysis of the similarities and differences that arose.  ...  By 1980 the understanding of acoustics for concert halls had reached an interesting stage.  ...  Here, both piezos are considered perfectly bonded to the beam and the Bernoulli-Euler hypothesis is used for the displacement field.  ... 
doi:10.1121/1.406641 fatcat:2ulfax5x7rg3nogxaiinu4epfe

Comparisons of auditorium acoustics measurements as a function of location in halls

John S. Bradley, A. C. Gade, Gary W. Siebein
1993 Journal of the Acoustical Society of America  
This paper will compare the results of room average data and several specific seat locations obtained from the two measurement systems with an analysis of the similarities and differences that arose.  ...  By 1980 the understanding of acoustics for concert halls had reached an interesting stage.  ...  Here, both piezos are considered perfectly bonded to the beam and the Bernoulli-Euler hypothesis is used for the displacement field.  ... 
doi:10.1121/1.406637 fatcat:qm3xseekvjgtpaucjdpbkm3o2y

Index: Volumes 21-30

1971 Proceedings of the American Mathematical Society  
equations 65H05 Single equations 65H10 Systems of equations 65J05 Numerical analysis in abstract spaces 65K05 Mathematical programming and optimization techniques [Computational aspects; for algorithms  ...  IP 65D99 None of the above, but in this section 65E05 Numerical methods in complex analysis (potential theory, etc.) [ For numerical methods in conformai mapping, see 30A28. j 65Fxx Numerical  ... 
doi:10.1090/s0002-9939-71-99972-2 fatcat:fh3qmht755dope6cfo3csgim2i