Refinement of Estimates of Sums of Sine Series with Monotone Coefficients and Cosine Series with Convex Coefficients

2021 ◽  
Vol 109 (5-6) ◽  
pp. 808-818
Author(s):  
A. Yu. Popov
Keyword(s):  
Sine Series ◽  
Cosine Series ◽  
Monotone Coefficients

scholarly journals L1-convergence of double trigonometric series

Filomat ◽  
2019 ◽  
Vol 33 (12) ◽  
pp. 3759-3771
Author(s):  
Karanvir Singh ◽  
Kanak Modi
Keyword(s):  
Trigonometric Series ◽  
Bounded Variation ◽  
Pointwise Convergence ◽  
Null Sequence ◽  
Sine Series ◽  
Double Trigonometric Series ◽  
L1 Norm ◽  
Cosine Series

In this paper we study the pointwise convergence and convergence in L1-norm of double trigonometric series whose coefficients form a null sequence of bounded variation of order (p,0),(0,p) and (p,p) with the weight (jk)p-1 for some integer p > 1. The double trigonometric series in this paper represents double cosine series, double sine series and double cosine sine series. Our results extend the results of Young [9], Kolmogorov [4] in the sense of single trigonometric series to double trigonometric series and of M?ricz [6,7] in the sense of higher values of p.

Reducing the near boundary errors of nonhomogeneous heat equations by boundary consistent methods

2020 ◽  
Author(s):  
Chein-Shan Liu ◽  
Chih-Wen Chang
Keyword(s):  
Heat Equations ◽  
Series Method ◽  
Sine Series ◽  
Fourier Cosine ◽  
Cosine Series ◽  
Fourier Sine ◽  
Fourier Cosine Series ◽  
Fourier Sine Series ◽  
Gibbs Phenomena ◽  
Nonhomogeneous Heat

Abstract In the paper, we point out a drawback of the Fourier sine series method to represent a given odd function, where the boundary Gibbs phenomena would occur when the boundary values of the function are non-zero. We modify the Fourier sine series method by considering the consistent conditions on the boundaries, which can improve the accuracy near the boundaries. The modifications are extended to the Fourier cosine series and the Fourier series. Then, novel boundary consistent methods are developed to solve the 1D and 2D heat equations. Numerical examples confirm the accuracy of the boundary consistent methods, accounting for the non-zeros of the source terms and considering the consistency of heat equations on the boundaries, which can not only overcome the near boundary errors but also improve the accuracy of solution about four orders in the entire domain, upon comparing to the conventional Fourier sine series method and Duhamel’s principle.

On Sine Series with Monotone Coefficients

1953 ◽  
Vol s1-28 (1) ◽  
pp. 102-104 ◽  
Author(s):  
Philip Hartman ◽  
Aurel Wintner
Keyword(s):  
Sine Series ◽  
Monotone Coefficients
Sign in / Sign up

Export Citation Format

Share Document