Open Access
2015 Windowed Fourier Frames to Approximate Two-Point Boundary Value Problems
Abdullah Aljouiee, Samir Kumar Bhowmik
Abstr. Appl. Anal. 2015: 1-7 (2015). DOI: 10.1155/2015/153010
Abstract

Boundary value problems arise while modeling various physical and engineering reality. In this communication we investigate windowed Fourier frames focusing two-point BVPs. We approximate BVPs using windowed Fourier frames. We present some numerical results to demonstrate the efficiency of such frame functions to approximate BVPs.

References

1.

A. Ashyralyev and O. Yildirim, “On stability of a third order of accuracy difference scheme for hyperbolic nonlocal BVP with self-adjoint operator,” Abstract and Applied Analysis, vol. 2013, Article ID 959216, 15 pages, 2013. MR3147785 07095537 A. Ashyralyev and O. Yildirim, “On stability of a third order of accuracy difference scheme for hyperbolic nonlocal BVP with self-adjoint operator,” Abstract and Applied Analysis, vol. 2013, Article ID 959216, 15 pages, 2013. MR3147785 07095537

2.

S. K. Bhowmik, “Tchebychev polynomial approximations for ${m}$th order boundary value problems,” International Journal of Pure and Applied Mathematics, vol. 98, no. 1, pp. 45–63, 2015. S. K. Bhowmik, “Tchebychev polynomial approximations for ${m}$th order boundary value problems,” International Journal of Pure and Applied Mathematics, vol. 98, no. 1, pp. 45–63, 2015.

3.

S. K. Bhowmik, F. M. Al Faqih, and N. Islam, “A note on some numerical approaches to solve a $\dot{\theta }$ neuron networks model,” Abstract and Applied Analysis, vol. 2014, Article ID 863842, 7 pages, 2014. 07023217 10.1155/2014/863842 S. K. Bhowmik, F. M. Al Faqih, and N. Islam, “A note on some numerical approaches to solve a $\dot{\theta }$ neuron networks model,” Abstract and Applied Analysis, vol. 2014, Article ID 863842, 7 pages, 2014. 07023217 10.1155/2014/863842

4.

S. Kumar, S. Dhawan, and S. Kapoor, “Numerical method for advection diffusion equation using fem and b-splines,” Journal of Computational Science, vol. 3, no. 5, pp. 429–437, 2012. S. Kumar, S. Dhawan, and S. Kapoor, “Numerical method for advection diffusion equation using fem and b-splines,” Journal of Computational Science, vol. 3, no. 5, pp. 429–437, 2012.

5.

S. Mallat, A Wavelet Tour of Signal Processing, Academic Press, Amsterdam, The Netherlands, 3rd edition, 2009. MR2479996 1170.94003 S. Mallat, A Wavelet Tour of Signal Processing, Academic Press, Amsterdam, The Netherlands, 3rd edition, 2009. MR2479996 1170.94003

6.

C. C. Stolk, “A fast method for linear waves based on geometrical optics,” SIAM Journal on Numerical Analysis, vol. 47, no. 2, pp. 1168–1194, 2009. MR2485449 1192.78004 10.1137/070698919 C. C. Stolk, “A fast method for linear waves based on geometrical optics,” SIAM Journal on Numerical Analysis, vol. 47, no. 2, pp. 1168–1194, 2009. MR2485449 1192.78004 10.1137/070698919

7.

S. K. Bhowmik and C. C. Stolk, “Preconditioners based on windowed Fourier frames applied to elliptic partial differential equations,” Journal of Pseudo-Differential Operators and Applications, vol. 2, no. 3, pp. 317–342, 2011. MR2831661 10.1007/s11868-011-0026-5 1255.42025 S. K. Bhowmik and C. C. Stolk, “Preconditioners based on windowed Fourier frames applied to elliptic partial differential equations,” Journal of Pseudo-Differential Operators and Applications, vol. 2, no. 3, pp. 317–342, 2011. MR2831661 10.1007/s11868-011-0026-5 1255.42025

8.

K. Gröchenig, Foundations of Time-Frequency Analysis, Birkhäuser, Boston, Mass, USA, 2000. MR1843717 0966.42020 K. Gröchenig, Foundations of Time-Frequency Analysis, Birkhäuser, Boston, Mass, USA, 2000. MR1843717 0966.42020

9.

O. Christensen, An Introduction to Frames and Riesz Bases, Birkhauser, 2004. \endinput 1348.42033 O. Christensen, An Introduction to Frames and Riesz Bases, Birkhauser, 2004. \endinput 1348.42033
Copyright © 2015 Hindawi
Abdullah Aljouiee and Samir Kumar Bhowmik "Windowed Fourier Frames to Approximate Two-Point Boundary Value Problems," Abstract and Applied Analysis 2015(none), 1-7, (2015). https://doi.org/10.1155/2015/153010
Published: 2015
Vol.2015 • 2015
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