ISSN (Print): 2372-2118

ISSN (Online): 2372-2126

Editor-in-Chief: Emanuele Galligani

Website: http://www.sciepub.com/journal/AJNA

   

Article

Construction of Optimal Quadrature Formula for Numerical Calculation of Fourier Coefficients in Sobolev Space L2(1)

1Department of Comptational Methods, Institute of Mathematics, National University of Uzbekistan, Tashkent, Uzbekistan


American Journal of Numerical Analysis. 2016, 4(1), 1-7
doi: 10.12691/ajna-4-1-1
Copyright © 2016 Science and Education Publishing

Cite this paper:
Nurali D. Boltaev, Abdullo R. Hayotov, Kholmat M. Shadimetov. Construction of Optimal Quadrature Formula for Numerical Calculation of Fourier Coefficients in Sobolev Space L2(1). American Journal of Numerical Analysis. 2016; 4(1):1-7. doi: 10.12691/ajna-4-1-1.

Correspondence to: Abdullo  R. Hayotov, Department of Comptational Methods, Institute of Mathematics, National University of Uzbekistan, Tashkent, Uzbekistan. Email: hayotov@mail.ru

Abstract

In the present paper the optimal quadrature formula for approximate evaluation of Fourier coefficients is constructed for functions of the space . At the same time the explicit formulas for optimal coefficients, which are very useful in applications, are obtained. The obtained formula is exact for constant. In particular, as consequences of the main result the new optimal quadrature formulas for approximate evaluation of integrals and are obtained. Furthermore, the order of convergence of the constructed optimal quadrature formula is studied.

Keywords

References

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Article

Dynamics of Kinks by Using Adomian Decomposition Method

1Department of Physics, Faculty of Basic Science, Chabahar Maritime University, Chabahar, Iran


American Journal of Numerical Analysis. 2016, 4(1), 8-10
doi: 10.12691/ajna-4-1-2
Copyright © 2016 Science and Education Publishing

Cite this paper:
Arash Ghahraman. Dynamics of Kinks by Using Adomian Decomposition Method. American Journal of Numerical Analysis. 2016; 4(1):8-10. doi: 10.12691/ajna-4-1-2.

Correspondence to: Arash  Ghahraman, Department of Physics, Faculty of Basic Science, Chabahar Maritime University, Chabahar, Iran. Email: arash.ghgood@gmail.com

Abstract

This paper studies nonlinear waves in the presence of weak external perturbation. Dynamical behavior of kink is examined. Adomian decomposition method is employed to study the kink-impurity interaction. As a result, an analytical approximate solution is derived. Then some of the first terms of the series solution are considered to show the kink behavior in the presence of impurity.

Keywords

References

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Article

New Constraction Seven Degree Spline Function to Solve Sencond Order Initial Value Problem

1Mathematics Department, School of Science, University of Sulaimani, Sulaimani, Kurdistan Region, Iraq

2Mathematics Department, College of Science, University of Garmian, Kalar, Kurdistan Region, Iraq


American Journal of Numerical Analysis. 2016, 4(1), 11-20
doi: 10.12691/ajna-4-1-3
Copyright © 2016 Science and Education Publishing

Cite this paper:
Karwan H.F. Jwamer, Najim Abdullah I.. New Constraction Seven Degree Spline Function to Solve Sencond Order Initial Value Problem. American Journal of Numerical Analysis. 2016; 4(1):11-20. doi: 10.12691/ajna-4-1-3.

Correspondence to: Karwan  H.F. Jwamer, Mathematics Department, School of Science, University of Sulaimani, Sulaimani, Kurdistan Region, Iraq. Email: karwan.jwamer@univsul.edu.iq

Abstract

Our paper dedicated to find approximate solution of second order initial value problem by seven degree lacunary spline function of type (0, 1, 6). The convergence analysis of given method has studied. Numerical illustrations have given with example for calculating absolute error between spline functions and exact solution of second order initial value problem with their derivatives.

Keywords

References

[1]  Abbas Y. Al Bayaty, Rostam K. Saeed, Faraidun K. Hama Salh “The Existence, Uniqueness and Error Bound of Approximation Spline Interpolation for Solving Second-Order Initial Value Problems” Journal of Mathematics and Statistics, Vol 5(2), pp.123-129, (2009).
 
[2]  Aryan Ali Muhammad ((Spline solution and Asymptotic Behaviors of Eigen values and Eigen function for some Types of Boundary value problem)) , A Thesis submitted to The Council of Faculty of science and science Education , school of science, University of Sulaimani in Pan till Fullfillment of the Requirements of the Degree of Doctor of Philosophy of science in Mathematics; January2013.
 
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[6]  J. Karwan Hama Faraj “Approximation Solution of second order Initial value problem by spline Function of degree seven”. Int. J. Contemp. Math. Science, Vol.5, 2010, no 46, 2293-2309.
 
[7]  Jwamer, K. H.-F. and R. G. Karim, 2010On Sixtic Lacunary Spline Solution of fourth Order Initial Value Problem. Asian Journal of Mathematics and Statistic, Pakistan,3 (3): 119-129.
 
[8]  Karwan H.F. Jawmer and Aryan Ali M. ((Second order Initial Value Problem and its Eight Degree spline solution)). world Applied science Journal17(12): 1694-1712, 2012.
 
[9]  L. L. Schumaker, Spline Function, Basic Theory, John Wiley, New York, 1981.
 
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[12]  R. K. Saeed, and K. H.-F. Jwamer, Lacunary interpolation by Spline Function (0, 1, 4) case, J. Dohuk Univ., Printed in Kurdistan Region, 4(2001), 193-196.
 
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