Yüksek Mertebeden Lineer Diferansiyel Fark Denklemlerinin Rezidüel Hata Tahminiyle Çözümü için Boubaker Polinom Yaklaşımı
Öz
Bu
çalışmanın temel amacı başlangıç-sınır koşulları altında fonksiyonel argümentli
yüksek mertebeden lineer diferansiyel-fark denklemlerinin çözümü için Boubaker
polinomlarını uygulamaktır. Kullandığımız teknik, aslında sıralama noktaları ile
birlikte kesilmiş Boubaker serisine ve bunların matris gösterimlerine
dayandırılır. Ayrıca, Ortalama-Değer Teoremini ve rezidüel fonksiyonu
kullanarak, etkili bir hata tahmin tekniği önerilir; metodun etkinliğini ve
uygulanabilirliğini göstermek için bazı
açıklayıcı örnekler sunulur.
Anahtar Kelimeler
Boubaker Polinomları ve Serileri Sıralama Noktaları Diferansiyel Fark Denklemleri Matris Metodu
Kaynakça
- Ablowitz, M., L., Ladik, J., F. (1976). A nonlinear difference scheme and inverse scattering, Stud. Appl. Math., 55, 213-229.
- Hu, X., B., Ma, W., X. (2002). Application of Hirota’s bilinear formalism to the Toeplitz lattice some special soliton – like solutions, Phys. Lett. A 293, 161-165.
- Fan, E. (2001). Soliton solutions for a generalized Hirota-Sotsuma coupled KdV equation a Coupled MKdV equation, Phys. Lett. A 282, 18-22.
- Dai, C., Zhang, J. (2006). Jacobian elliptic function method for nonlinear differential difference equations, Chaos, Soliton Fract. 27, 1042-1047.
- Elmer, C., E., Van Vleck,, E., S. (2001). Traveling wave solutions for Bistable Differential- Difference Equations with Periodic Diffusion, SIAM J. Appl. Math. 61(5), 1648-1679.
- Elmer, C., E., Van Vleck, E., S. (2002). A Variant of Newton’s Method for the Computation of Traveling Waves of Bistable Differential-Difference Equation, J. Dyn. Different. Equat. 14, 493-517.
- Arıkoğlu, A., Özkol, I. (2006). Solution of difference equations by using differential transform method, Appl. Math. Comput. 174, 1216-1228.
- Sezer, M., Gülsu, M. (2005). Polynomial solution of the most general linear Fredholm İntegro- differntial-difference equation by means of Taylor matrix method, Complex variables, 50(5), 367-382.
- Gülsu, M., Sezer, M. (2005). A method for the approximate solution of the high-order linear difference equations in terms of Taylor polynomials, Intern. J. Comput. Math. 82(5), 629-641.
- Saaty, TL. (1981). Modern nonlinear equations, Dover publications Inc., New York, P.225.
- Akkaya, T., Yalçınbaş, S., Sezer, M. (2013). Numeric solutions for the pantograph type delay differential equation using first Boubaker polynomials, Applied Mathematics and Computation 219, 9484–9492.
- Akgönüllü,N., Şahin, N., Sezer, M. (2011).A Hermite Collocation Method for the Approximate Solutions of High-Order Linear Fredholm Integro-Differential Equations, Numerical Methods Partial Differential Eq. 27: 1707–1721.
- Boubaker, K. (2007). Trends Appl. Sci. Res. On Modified Boubaker Polynomials: Some Differential and Analytical Properties of the New Polynomials Issued from an Attempt for Solving Bi-varied Heat Equation 2(6), (ss: 540–544).
- Akyuz-Dascioglu, A. (2006). A Chebyshev polynomial approach for linear Fredholm–Volterra Integro differential equations in the most general form, Appl Math Comput 181, 103–112.
- Yalçınbaş, S., and Sezer, M. (2006). A Taylor collocation method for the approximate solution of general linear Fredholm-Volterra integro-difference equations with mixed argument, Appl Math Comput 175, 675–690.
- Evans, D.J., Raslan, K.R, (2005). The Adomian decomposition method for solving delay differential equation, Int. J. Comput. Math. 82 (1), 49–54.
- Yalçınbas, S., Aynigül, M., Sezer, M. (2011). A collocation method using Hermite polynomials for approximate solution ofpantograph equations, J. Franklin Inst. 348 (6),1128–1139.
- Sezer, M., Akyuz-Dascioglu, A. (2006). Taylor polynomial solutions of general linear differential–difference equations with variable coefficients , Appl Math Comput 174, 1526–1538.
- Arıkoğlu, A.,, I. (2006). Solution of difference equations by using differential transform method, Appl. Matth. Comput. 174, 1216-1228.
Boubaker Polynomial Approach for Solving High-Order Linear Differential-Difference Equations with Residual Error Estimation
Öz
The main aim of this study is to apply the Boubaker polynomials for the
solution of high-order linear differential-difference equations with functional
arguments under the initial-boundary conditions. The technique we have used is
essentially based on the truncated Boubaker series and its matrix
representations together with collocation points. Also, by using the Mean-Volue
Theorem and residual function, an efficient error estimation technique is
proposed and some illustrative examples are presented to demonstrate the
validity and applicability of the method.
Anahtar Kelimeler
Boubaker Polynomials and Series Collocation Points Differential-Difference Equations Matrix Method
Kaynakça
- Ablowitz, M., L., Ladik, J., F. (1976). A nonlinear difference scheme and inverse scattering, Stud. Appl. Math., 55, 213-229.
- Hu, X., B., Ma, W., X. (2002). Application of Hirota’s bilinear formalism to the Toeplitz lattice some special soliton – like solutions, Phys. Lett. A 293, 161-165.
- Fan, E. (2001). Soliton solutions for a generalized Hirota-Sotsuma coupled KdV equation a Coupled MKdV equation, Phys. Lett. A 282, 18-22.
- Dai, C., Zhang, J. (2006). Jacobian elliptic function method for nonlinear differential difference equations, Chaos, Soliton Fract. 27, 1042-1047.
- Elmer, C., E., Van Vleck,, E., S. (2001). Traveling wave solutions for Bistable Differential- Difference Equations with Periodic Diffusion, SIAM J. Appl. Math. 61(5), 1648-1679.
- Elmer, C., E., Van Vleck, E., S. (2002). A Variant of Newton’s Method for the Computation of Traveling Waves of Bistable Differential-Difference Equation, J. Dyn. Different. Equat. 14, 493-517.
- Arıkoğlu, A., Özkol, I. (2006). Solution of difference equations by using differential transform method, Appl. Math. Comput. 174, 1216-1228.
- Sezer, M., Gülsu, M. (2005). Polynomial solution of the most general linear Fredholm İntegro- differntial-difference equation by means of Taylor matrix method, Complex variables, 50(5), 367-382.
- Gülsu, M., Sezer, M. (2005). A method for the approximate solution of the high-order linear difference equations in terms of Taylor polynomials, Intern. J. Comput. Math. 82(5), 629-641.
- Saaty, TL. (1981). Modern nonlinear equations, Dover publications Inc., New York, P.225.
- Akkaya, T., Yalçınbaş, S., Sezer, M. (2013). Numeric solutions for the pantograph type delay differential equation using first Boubaker polynomials, Applied Mathematics and Computation 219, 9484–9492.
- Akgönüllü,N., Şahin, N., Sezer, M. (2011).A Hermite Collocation Method for the Approximate Solutions of High-Order Linear Fredholm Integro-Differential Equations, Numerical Methods Partial Differential Eq. 27: 1707–1721.
- Boubaker, K. (2007). Trends Appl. Sci. Res. On Modified Boubaker Polynomials: Some Differential and Analytical Properties of the New Polynomials Issued from an Attempt for Solving Bi-varied Heat Equation 2(6), (ss: 540–544).
- Akyuz-Dascioglu, A. (2006). A Chebyshev polynomial approach for linear Fredholm–Volterra Integro differential equations in the most general form, Appl Math Comput 181, 103–112.
- Yalçınbaş, S., and Sezer, M. (2006). A Taylor collocation method for the approximate solution of general linear Fredholm-Volterra integro-difference equations with mixed argument, Appl Math Comput 175, 675–690.
- Evans, D.J., Raslan, K.R, (2005). The Adomian decomposition method for solving delay differential equation, Int. J. Comput. Math. 82 (1), 49–54.
- Yalçınbas, S., Aynigül, M., Sezer, M. (2011). A collocation method using Hermite polynomials for approximate solution ofpantograph equations, J. Franklin Inst. 348 (6),1128–1139.
- Sezer, M., Akyuz-Dascioglu, A. (2006). Taylor polynomial solutions of general linear differential–difference equations with variable coefficients , Appl Math Comput 174, 1526–1538.
- Arıkoğlu, A.,, I. (2006). Solution of difference equations by using differential transform method, Appl. Matth. Comput. 174, 1216-1228.
Ayrıntılar
| Konular | Matematik |
|---|---|
| Bölüm | Matematik |
| Yazarlar | |
| Yayımlanma Tarihi | 27 Aralık 2016 |
| Yayımlandığı Sayı | Yıl 2016 Cilt: 1 Sayı: 1 |
