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Sayısal İntegral Metodu ile Singüler Pertürbe Multi-Point Sınır Değer Problemlerinin Sayısal Çözümü

Year 2020, Volume: 9 Issue: 1, 157 - 167, 13.03.2020
https://doi.org/10.17798/bitlisfen.662732

Abstract

Bu çalışmada, sağ ya da sol sınır katlarına sahip singüler pertürbe multi-point sınır değer probleminin çözümü için düzgün şebeke üzerinde sayısal integral metodu sunulur. Bu metodun yanında yamuk metodu, sonlu fark metodu ve Thomas algoritmasından yararlanılır. Önerilen yöntemin kararlılığı ve yakınsaklığı analiz edilir. Son olarak da, yöntemin doğruluğunu ve verimliliğini gösteren örnek uygulamalar yapılır.

References

  • Referans 1 Amiraliyev G.M., Cakir M. 2002. Numerical Solution of the Singularly Perturbed Problem with Nonlocal Condition, Applied Mathematics and Mechanics, 23: (7), 755-764. Referans 2 Cakir M., Arslan D. 2016. A Numerical Method for Nonlinear Singularly Perturbed Multi-Point Boundary Value Problem, Journal of Applied Mathematics and Phyics, 4, 1143-1156. Referans 3 Cakir M., Arslan D. 2016. Numerical Solution of the Nonlocal Singularly Perturbed Problem, International Journal of Modern Research in Engineering and Technology, 1: (5), 13-24. Referans 4 Cakir M., Arslan D. 2016. Finite Difference Method for Nonlocal Singularly Perturbed Problem, International Journal of Modern Research in Engineering and Technology, 1: (5), 25-39. Referans 5 Arslan D. 2017. Finite Difference Method for Solving Singularly Perturbed Multi-Point Boundary Value Problem, Journal of the Institute of Natural and Applied Sciences, 22: (2), 64-75. Referans 6 Cakir M., Amiraliyev G.M. 2007. Numerical Solution of the Singularly Perturbed Three-Point Boundary Value Problem, International Journal of Computer Mathematics, 84: (10), 1465-1481. Referans 7 Chegis R. 1988. The Numerical Solution of Problems with Small Parameter at Higher Derivatives and Nonlocal Conditions, Lietuvas Matematica Rinkinys, (in Russian), 28, 144-152. Referans 8 Arslan D. 2019. Stability and Convergence Analysis on Shishkin Mesh for a Nonlinear Singularly Perturbed Problem with Three-Point Boundary Condition, Quaestiones Mathematicae, 1-14. Referans 9 Arslan D. 2019. A Numerical Solution Study on Singularly Perturbed Convection-Diffusion Nonlocal Boundary Value Problem, Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 68 (2): 1482-1491. Referans 10 Gupta C.P., Trofimchuk S.I. 1997. A Sharper Condition for the Solvability of a Three-Point Second Order Boundary Value Problem, Journal of Mathematical Analysis and Applications, 205: 586-597. Referans 11 Herceg D., Surla K. 1991. Solving a Nonlocal Singularly Perturbed Nonlocal Problem by Splines in Tension, Univ. u Novom Sadu Zb. Rad. Prirod.-Mat. Fak. Ser. Math., 21: (2), 119- 132. Referans 12 Farell P.A., Miller J.J.H., O.Riordan E., Shishkin G.I. 1996. A Uniformly Convergent Finite Difference Scheme for a Singularly Perturbed Semilinear Equation, SIAM Journal on Numerical Analysis, 33: 1135-1149. Referans 13 Miller J.J.H.,, O.Riordan E., Shishkin G.I. 1996. Fitted Numerical Methods for Singular Perturbation Problems, World Scientic, Singapore. Referans 14 Nayfeh A.H. 1993. Introduction to Perturbation Techniques, Wiley, New York. Referans 15 Reddy Y.N. 1990. A Numerical Integration Method for Solving Singular Perturbation Problems, Applied Mathematics and Computation, 37: 83-95. Referans 16 Andargie A., Reddy Y.N. 2008. Numerical Integration Method for Singular Perturbation Problems with Mixed Boundary Conditions, J. Appl. Math. & Informatics, 26 (5-6): 1273-1287. Referans 17 Soujanya G., Phnaeendra K. 2015. Numerical Intergration Method for Singular-Singularly Perturbed Two- Point Boundary Value Problems, Procedia Engineering, 127: 545-552. Referans 18 Ranjan R., Prasad H.S. 2018. An Efficient Method of Numerical Integration for a Class of Singularly Perturbed Two Point Boundary Value Problems, Wseas Transactions On Mathematics, 17: 265-273. Referans 19 Amirali G., Amirali I. 2018. Nümerik Analiz Teori ve Uygulamalarla, Seçkin Yayıncılık, Ankara, Türkiye. Referans 20 Altun Y. 2019. New Results on the Exponential Stability of Solutions of Periodic Nonlinear Neutral Differential Systems, Dynamic Systems and Applications, 28: 303-316. Referans 21 Cimen E. 2017. A Priori Estimates for Solution of Singularly Perturbed Boundary Value Problem with Delay in Convection Term, J. Math. Anal., 8 (1): 202-211.
Year 2020, Volume: 9 Issue: 1, 157 - 167, 13.03.2020
https://doi.org/10.17798/bitlisfen.662732

Abstract

References

  • Referans 1 Amiraliyev G.M., Cakir M. 2002. Numerical Solution of the Singularly Perturbed Problem with Nonlocal Condition, Applied Mathematics and Mechanics, 23: (7), 755-764. Referans 2 Cakir M., Arslan D. 2016. A Numerical Method for Nonlinear Singularly Perturbed Multi-Point Boundary Value Problem, Journal of Applied Mathematics and Phyics, 4, 1143-1156. Referans 3 Cakir M., Arslan D. 2016. Numerical Solution of the Nonlocal Singularly Perturbed Problem, International Journal of Modern Research in Engineering and Technology, 1: (5), 13-24. Referans 4 Cakir M., Arslan D. 2016. Finite Difference Method for Nonlocal Singularly Perturbed Problem, International Journal of Modern Research in Engineering and Technology, 1: (5), 25-39. Referans 5 Arslan D. 2017. Finite Difference Method for Solving Singularly Perturbed Multi-Point Boundary Value Problem, Journal of the Institute of Natural and Applied Sciences, 22: (2), 64-75. Referans 6 Cakir M., Amiraliyev G.M. 2007. Numerical Solution of the Singularly Perturbed Three-Point Boundary Value Problem, International Journal of Computer Mathematics, 84: (10), 1465-1481. Referans 7 Chegis R. 1988. The Numerical Solution of Problems with Small Parameter at Higher Derivatives and Nonlocal Conditions, Lietuvas Matematica Rinkinys, (in Russian), 28, 144-152. Referans 8 Arslan D. 2019. Stability and Convergence Analysis on Shishkin Mesh for a Nonlinear Singularly Perturbed Problem with Three-Point Boundary Condition, Quaestiones Mathematicae, 1-14. Referans 9 Arslan D. 2019. A Numerical Solution Study on Singularly Perturbed Convection-Diffusion Nonlocal Boundary Value Problem, Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 68 (2): 1482-1491. Referans 10 Gupta C.P., Trofimchuk S.I. 1997. A Sharper Condition for the Solvability of a Three-Point Second Order Boundary Value Problem, Journal of Mathematical Analysis and Applications, 205: 586-597. Referans 11 Herceg D., Surla K. 1991. Solving a Nonlocal Singularly Perturbed Nonlocal Problem by Splines in Tension, Univ. u Novom Sadu Zb. Rad. Prirod.-Mat. Fak. Ser. Math., 21: (2), 119- 132. Referans 12 Farell P.A., Miller J.J.H., O.Riordan E., Shishkin G.I. 1996. A Uniformly Convergent Finite Difference Scheme for a Singularly Perturbed Semilinear Equation, SIAM Journal on Numerical Analysis, 33: 1135-1149. Referans 13 Miller J.J.H.,, O.Riordan E., Shishkin G.I. 1996. Fitted Numerical Methods for Singular Perturbation Problems, World Scientic, Singapore. Referans 14 Nayfeh A.H. 1993. Introduction to Perturbation Techniques, Wiley, New York. Referans 15 Reddy Y.N. 1990. A Numerical Integration Method for Solving Singular Perturbation Problems, Applied Mathematics and Computation, 37: 83-95. Referans 16 Andargie A., Reddy Y.N. 2008. Numerical Integration Method for Singular Perturbation Problems with Mixed Boundary Conditions, J. Appl. Math. & Informatics, 26 (5-6): 1273-1287. Referans 17 Soujanya G., Phnaeendra K. 2015. Numerical Intergration Method for Singular-Singularly Perturbed Two- Point Boundary Value Problems, Procedia Engineering, 127: 545-552. Referans 18 Ranjan R., Prasad H.S. 2018. An Efficient Method of Numerical Integration for a Class of Singularly Perturbed Two Point Boundary Value Problems, Wseas Transactions On Mathematics, 17: 265-273. Referans 19 Amirali G., Amirali I. 2018. Nümerik Analiz Teori ve Uygulamalarla, Seçkin Yayıncılık, Ankara, Türkiye. Referans 20 Altun Y. 2019. New Results on the Exponential Stability of Solutions of Periodic Nonlinear Neutral Differential Systems, Dynamic Systems and Applications, 28: 303-316. Referans 21 Cimen E. 2017. A Priori Estimates for Solution of Singularly Perturbed Boundary Value Problem with Delay in Convection Term, J. Math. Anal., 8 (1): 202-211.
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Details

Primary Language Turkish
Subjects Engineering
Journal Section Araştırma Makalesi
Authors

Derya Arslan 0000-0001-6138-0607

Publication Date March 13, 2020
Submission Date December 20, 2019
Acceptance Date February 4, 2020
Published in Issue Year 2020 Volume: 9 Issue: 1

Cite

IEEE D. Arslan, “Sayısal İntegral Metodu ile Singüler Pertürbe Multi-Point Sınır Değer Problemlerinin Sayısal Çözümü”, Bitlis Eren Üniversitesi Fen Bilimleri Dergisi, vol. 9, no. 1, pp. 157–167, 2020, doi: 10.17798/bitlisfen.662732.

Bitlis Eren University
Journal of Science Editor
Bitlis Eren University Graduate Institute
Bes Minare Mah. Ahmet Eren Bulvari, Merkez Kampus, 13000 BITLIS