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Yıl 2018, , 25 - 35, 30.06.2018

İbrahim Çelik

https://doi.org/10.33401/fujma.421996
Cited By: 2

Öz

Kaynakça

  • [1] A, Guezane-Lakoud, A. Frioui, Nonlinear three point boundary-value problem, Sarajevo Journal of Mathematics,8/20 (2012), 101-106.
  • [2] B. Aksoylu, T. Mengesha, Results on nonlocal boundary value problems, Numerical functional analysis and optimization, 31/12 (2010), 1301-1317.
  • [3] J. Henderson, CJ.Kunkel, Uniqueness of solution of linear nonlocal boundary value problems, Applied Mathematics Letters, 21 (2008), 1053-1056.
  • [4] X. Xue, Nonlinear differential equations with nonlocal conditions in Banach spaces, Nonlinear Analysis: Theory, Methods and Applications , 63 (2005), 575-586.
  • [5] P. Babak, Nonlocal initial problems for coupled reaction-diffusion systems and their applications, Nonlinear analysis: real world applications , 8 (2007), 980-996.
  • [6] J. Liang, TJ. Xiao, Semilinear integrodifferential equations with nonlocal initial conditions, Computers and Mathematics with Applications , 47 (2004), 863-875.
  • [7] F. Geng, M. Cui, A repreducing kernel method for solving nonlocal fractional boundary value problems, Applied Mathematics Letters, (2012), 818-823.
  • [8] Y. Zhou, F. Jiao, Nonlocal Cauchy problem for fractional evolution equations, Nonlinear analysis: real world applications , 11 (2010), 4465-4475.
  • [9] Lentini M, Pereyra V. A variable order finite difference method for nonlinear multipoint boundary value problems. Mathematics of Computation 1974; 28: 981–1003.
  • [10] MK. Kwong, The shooting method and multiple solutions of two/multi-point BVPs of second-order ODE, Electronic Journal of Qualitative Theory of Differential Equations, 6 (2006), 1-14.
  • [11] YK. Zou, QW. Hu and R. Zhang, On numerical studies of multi-point boundary value problem and its fold bifurcation, Applied Mathematics and Computation, 185 (2007), 527-537.
  • [12] M. Tatari, M. Dehghan, The use of the Adomian decomposition method for solving multipoint boundary value problems, Physical Scripta, 73 (2006), 672-676.
  • [13] M. Tatari, M. Dehghan, An efficient method for solving multi-point boundary value problems and applications in physics, Journal of Vibration and Control, (2011), 1116-1124.
  • [14] M. Dehghan, F. Shakeri, A semi-numerical technique for solving the multi-point boundary value problems and engineering applications, International Journal of Numerical Methods for Heat and Fluid Flow, 21 (2011), 794-809.
  • [15] A. Saadatmandi, M. Dehghan, The use of Sinc-collocation method for solving multi-point boundary value problems, Communications in Nonlinear Science and Numerical Simulation, 17 (2012), 593-601.
  • [16] LJ. Xie, CL. Zhou, S. Xu, A new algorithm based on differential transform method for solving multi-point boundary value problems, International Journal of Computer Mathematics (2015); 1-14
  • [17] J. Ali, S. Islam, S. Islam and G. Zaman, The solution of multipoint boundary value problems by the optimal homotopy asymptotic method, Computers and Mathematics with Applications, 59/6 (2010), 2000-2006.
  • [18] FZ. Geng, MG. Cui, Multi-point boundary value problem for optimal bridge design, International Journal of Computer Mathematics, 87 (2010), 1051-1056.
  • [19] Y. Lin, J. Lin, A numerical algorithm for solving a class of linear nonlocal boundary value problems, Applied Mathematics Letters, 23 (2010), 997-1002.
  • [20] XY. Li, BY. Wu, Reproducing kernel method for singular fourth order four-point boundary value problems,Bulletin of the Malaysian Mathematical Sciences Society Second Series, 34/1 (2011), 147-151.
  • [21] B. Sun, Y. Aijun and G. Weigao, Successive iteration and positive solutions for some second-order three-point p-Laplacian boundary value problems, Mathematical and Computer Modelling, 50/3 (2009), 344-350.
  • [22] M. Behroozifar, Spectral method for solving high order nonlinear boundary value problems via operational matrices, BIT Numerical Mathematics, 55/4 (2015), 901-925
  • [23] D. Tzanetis, P. Vlamos, A nonlocal problem modelling ohmic heating with variable thermal conductivity, Nonlinear analysis: real world applications , 2/4 (2001), 443-454.
  • [24] M.Bogoya, A. Cesar and S. Gomez, On a nonlocal diffusion model with Neumann boundary conditions, Nonlinear Analysis: Theory, Methods and Applications, 75/6 (2012), 3198-3209.
  • [25] CV. Pao, Asymptotic behavior of solutions of reaction-diffusion equations with nonlocal boundary conditions, Journal of Computational and Applied Mathematics, 88 (1998), 225-238.
  • [26] CV. Pao , YM. Wang, Nonlinear fourth-order elliptic equations with nonlocal boundary conditions, Journal of Mathematical Analysis and Applications, 372 (2010), 351-365.
  • [27] CV. Pao , YM. Wang, Numerical methods for fourth-order elliptic equations with nonlocal boundary conditions, Journal of Computational and Applied Mathematics, 292 (2016), 447-468.
  • [28] M. Razzaghi, S. Yousefi, Legendre wavelets direct method for variational problems, Mathematics and Computers in Simulation, 53 (2000) 185-192.
  • [29] M. Razzaghi, S. Yousefi, Legendre wavelets operational matrix of integration, International Journal of Systems Science , 32/4 (2001) 495–502.
  • [30] E, Babolian, F. Fattahzadeh, Numerical solution of differential equations by using Chebyshev wavelet operational matrix of integration, Applied Mathematics and Computation 188 (2007), 417-426.
  • [31] MT. Kajania, AH. Vencheha and M.Ghasemib, The Chebyshev wavelets operational matrix of integration and product operation matrix, International Journal of Computer Mathematics, 86/7 (2009), 1118-1125
  • [32] İ. Çelik, Numerical Solution of Differential Equations by Using Chebyshev Wavelet Collocation Method, Cankaya University Journal of Science and Engineering., 10/2 (2013), 169-184.
  • [33] İ. Çelik, Chebyshev Wavelet Collocation Method for Solving Generalized Burgers-Huxley Equation, Mathematical Methods in the Applied Sciences, 39/3 (2016), 366-377.
  • [34] I. Daubechies, Ten lectures on wavelets , SIAM, Philadelphia,PA (1992)
  • [35] L, Fox, IB. Parker,Chebyshev polynomials in numerical analysis, Oxford University Press, London (1968)
  • [36] H. Adibi, P. Assari, Chebyshev wavelet method for numerical solution of Fredholm integral equations of the first kind, Mathematical Problems in Engineering, Article ID 138408 (2010), p 17
  • [37] C. Yang, J.Hou, Chebyshev wavelets method for solving Bratu’s problem, Boundary Value Problems, 2013 (2013), 142

Chebyshev Wavelet collocation method for solving a class of linear and nonlinear nonlocal boundary value problems

Yıl 2018, , 25 - 35, 30.06.2018

İbrahim Çelik

https://doi.org/10.33401/fujma.421996
Cited By: 2

Öz

This study proposes the Chebyshev Wavelet Colocation method for solving a class of rth-order Boundary-Value Problems (BVPs) with nonlocal boundary conditions. This method is an extension of the Chebyshev wavelet method to the linear and nonlinear BVPs with a class of nonlocal boundary conditions. In this study, the method is tested on second and fourth-order BVPs and approximate solutions are compared with the existing methods in the literature and analytical solutions. The proposed method has promising results in terms of the accuracy.

Anahtar Kelimeler

Approximate solution Boundary-value problems Chebyshev Wavelet Colocation method Nonlocal boundary conditions

Kaynakça

  • [1] A, Guezane-Lakoud, A. Frioui, Nonlinear three point boundary-value problem, Sarajevo Journal of Mathematics,8/20 (2012), 101-106.
  • [2] B. Aksoylu, T. Mengesha, Results on nonlocal boundary value problems, Numerical functional analysis and optimization, 31/12 (2010), 1301-1317.
  • [3] J. Henderson, CJ.Kunkel, Uniqueness of solution of linear nonlocal boundary value problems, Applied Mathematics Letters, 21 (2008), 1053-1056.
  • [4] X. Xue, Nonlinear differential equations with nonlocal conditions in Banach spaces, Nonlinear Analysis: Theory, Methods and Applications , 63 (2005), 575-586.
  • [5] P. Babak, Nonlocal initial problems for coupled reaction-diffusion systems and their applications, Nonlinear analysis: real world applications , 8 (2007), 980-996.
  • [6] J. Liang, TJ. Xiao, Semilinear integrodifferential equations with nonlocal initial conditions, Computers and Mathematics with Applications , 47 (2004), 863-875.
  • [7] F. Geng, M. Cui, A repreducing kernel method for solving nonlocal fractional boundary value problems, Applied Mathematics Letters, (2012), 818-823.
  • [8] Y. Zhou, F. Jiao, Nonlocal Cauchy problem for fractional evolution equations, Nonlinear analysis: real world applications , 11 (2010), 4465-4475.
  • [9] Lentini M, Pereyra V. A variable order finite difference method for nonlinear multipoint boundary value problems. Mathematics of Computation 1974; 28: 981–1003.
  • [10] MK. Kwong, The shooting method and multiple solutions of two/multi-point BVPs of second-order ODE, Electronic Journal of Qualitative Theory of Differential Equations, 6 (2006), 1-14.
  • [11] YK. Zou, QW. Hu and R. Zhang, On numerical studies of multi-point boundary value problem and its fold bifurcation, Applied Mathematics and Computation, 185 (2007), 527-537.
  • [12] M. Tatari, M. Dehghan, The use of the Adomian decomposition method for solving multipoint boundary value problems, Physical Scripta, 73 (2006), 672-676.
  • [13] M. Tatari, M. Dehghan, An efficient method for solving multi-point boundary value problems and applications in physics, Journal of Vibration and Control, (2011), 1116-1124.
  • [14] M. Dehghan, F. Shakeri, A semi-numerical technique for solving the multi-point boundary value problems and engineering applications, International Journal of Numerical Methods for Heat and Fluid Flow, 21 (2011), 794-809.
  • [15] A. Saadatmandi, M. Dehghan, The use of Sinc-collocation method for solving multi-point boundary value problems, Communications in Nonlinear Science and Numerical Simulation, 17 (2012), 593-601.
  • [16] LJ. Xie, CL. Zhou, S. Xu, A new algorithm based on differential transform method for solving multi-point boundary value problems, International Journal of Computer Mathematics (2015); 1-14
  • [17] J. Ali, S. Islam, S. Islam and G. Zaman, The solution of multipoint boundary value problems by the optimal homotopy asymptotic method, Computers and Mathematics with Applications, 59/6 (2010), 2000-2006.
  • [18] FZ. Geng, MG. Cui, Multi-point boundary value problem for optimal bridge design, International Journal of Computer Mathematics, 87 (2010), 1051-1056.
  • [19] Y. Lin, J. Lin, A numerical algorithm for solving a class of linear nonlocal boundary value problems, Applied Mathematics Letters, 23 (2010), 997-1002.
  • [20] XY. Li, BY. Wu, Reproducing kernel method for singular fourth order four-point boundary value problems,Bulletin of the Malaysian Mathematical Sciences Society Second Series, 34/1 (2011), 147-151.
  • [21] B. Sun, Y. Aijun and G. Weigao, Successive iteration and positive solutions for some second-order three-point p-Laplacian boundary value problems, Mathematical and Computer Modelling, 50/3 (2009), 344-350.
  • [22] M. Behroozifar, Spectral method for solving high order nonlinear boundary value problems via operational matrices, BIT Numerical Mathematics, 55/4 (2015), 901-925
  • [23] D. Tzanetis, P. Vlamos, A nonlocal problem modelling ohmic heating with variable thermal conductivity, Nonlinear analysis: real world applications , 2/4 (2001), 443-454.
  • [24] M.Bogoya, A. Cesar and S. Gomez, On a nonlocal diffusion model with Neumann boundary conditions, Nonlinear Analysis: Theory, Methods and Applications, 75/6 (2012), 3198-3209.
  • [25] CV. Pao, Asymptotic behavior of solutions of reaction-diffusion equations with nonlocal boundary conditions, Journal of Computational and Applied Mathematics, 88 (1998), 225-238.
  • [26] CV. Pao , YM. Wang, Nonlinear fourth-order elliptic equations with nonlocal boundary conditions, Journal of Mathematical Analysis and Applications, 372 (2010), 351-365.
  • [27] CV. Pao , YM. Wang, Numerical methods for fourth-order elliptic equations with nonlocal boundary conditions, Journal of Computational and Applied Mathematics, 292 (2016), 447-468.
  • [28] M. Razzaghi, S. Yousefi, Legendre wavelets direct method for variational problems, Mathematics and Computers in Simulation, 53 (2000) 185-192.
  • [29] M. Razzaghi, S. Yousefi, Legendre wavelets operational matrix of integration, International Journal of Systems Science , 32/4 (2001) 495–502.
  • [30] E, Babolian, F. Fattahzadeh, Numerical solution of differential equations by using Chebyshev wavelet operational matrix of integration, Applied Mathematics and Computation 188 (2007), 417-426.
  • [31] MT. Kajania, AH. Vencheha and M.Ghasemib, The Chebyshev wavelets operational matrix of integration and product operation matrix, International Journal of Computer Mathematics, 86/7 (2009), 1118-1125
  • [32] İ. Çelik, Numerical Solution of Differential Equations by Using Chebyshev Wavelet Collocation Method, Cankaya University Journal of Science and Engineering., 10/2 (2013), 169-184.
  • [33] İ. Çelik, Chebyshev Wavelet Collocation Method for Solving Generalized Burgers-Huxley Equation, Mathematical Methods in the Applied Sciences, 39/3 (2016), 366-377.
  • [34] I. Daubechies, Ten lectures on wavelets , SIAM, Philadelphia,PA (1992)
  • [35] L, Fox, IB. Parker,Chebyshev polynomials in numerical analysis, Oxford University Press, London (1968)
  • [36] H. Adibi, P. Assari, Chebyshev wavelet method for numerical solution of Fredholm integral equations of the first kind, Mathematical Problems in Engineering, Article ID 138408 (2010), p 17
  • [37] C. Yang, J.Hou, Chebyshev wavelets method for solving Bratu’s problem, Boundary Value Problems, 2013 (2013), 142
Toplam 37 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Makaleler
Yazarlar

İbrahim Çelik

Yayımlanma Tarihi 30 Haziran 2018
Gönderilme Tarihi 8 Mayıs 2018
Kabul Tarihi 21 Haziran 2018
Yayımlandığı Sayı Yıl 2018

Kaynak Göster

APA Çelik, İ. (2018). Chebyshev Wavelet collocation method for solving a class of linear and nonlinear nonlocal boundary value problems. Fundamental Journal of Mathematics and Applications, 1(1), 25-35. https://doi.org/10.33401/fujma.421996
AMA Çelik İ. Chebyshev Wavelet collocation method for solving a class of linear and nonlinear nonlocal boundary value problems. Fundam. J. Math. Appl. Haziran 2018;1(1):25-35. doi:10.33401/fujma.421996
Chicago Çelik, İbrahim. “Chebyshev Wavelet Collocation Method for Solving a Class of Linear and Nonlinear Nonlocal Boundary Value Problems”. Fundamental Journal of Mathematics and Applications 1, sy. 1 (Haziran 2018): 25-35. https://doi.org/10.33401/fujma.421996.
EndNote Çelik İ (01 Haziran 2018) Chebyshev Wavelet collocation method for solving a class of linear and nonlinear nonlocal boundary value problems. Fundamental Journal of Mathematics and Applications 1 1 25–35.
IEEE İ. Çelik, “Chebyshev Wavelet collocation method for solving a class of linear and nonlinear nonlocal boundary value problems”, Fundam. J. Math. Appl., c. 1, sy. 1, ss. 25–35, 2018, doi: 10.33401/fujma.421996.
ISNAD Çelik, İbrahim. “Chebyshev Wavelet Collocation Method for Solving a Class of Linear and Nonlinear Nonlocal Boundary Value Problems”. Fundamental Journal of Mathematics and Applications 1/1 (Haziran 2018), 25-35. https://doi.org/10.33401/fujma.421996.
JAMA Çelik İ. Chebyshev Wavelet collocation method for solving a class of linear and nonlinear nonlocal boundary value problems. Fundam. J. Math. Appl. 2018;1:25–35.
MLA Çelik, İbrahim. “Chebyshev Wavelet Collocation Method for Solving a Class of Linear and Nonlinear Nonlocal Boundary Value Problems”. Fundamental Journal of Mathematics and Applications, c. 1, sy. 1, 2018, ss. 25-35, doi:10.33401/fujma.421996.
Vancouver Çelik İ. Chebyshev Wavelet collocation method for solving a class of linear and nonlinear nonlocal boundary value problems. Fundam. J. Math. Appl. 2018;1(1):25-3.

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