An efficient dynamical systems method for solving singularly perturbed integral equations with noise

Computers and Mathematics with Applications

Volumn 58, Issue 7, 2009, Pages 1418-1424

  Sweilam, N H ^a   Nagy, A M ^b   Alnasr, M H ^c  

^a CAIRO UNIVERSITY   (Egypt)

^b BENHA UNIVERSITY   (Egypt)

^c Qatar University   (Qatar)

Author keywords

Dynamical systems method (DSM); Ill posed problems; Variational regularization method (VRM)

Indexed keywords

DYNAMICAL SYSTEMS METHOD; DYNAMICAL SYSTEMS METHOD (DSM); EXACT SOLUTION; ILL POSED PROBLEM; ILL-POSED PROBLEMS; LARGE SIZES; MODEL PROBLEMS; NUMERICAL SOLUTION; SINGULARLY PERTURBED; VARIATIONAL REGULARIZATION; VARIATIONAL REGULARIZATION METHOD (VRM);

DYNAMIC LOADS; ELECTRIC LOAD MANAGEMENT; PERTURBATION TECHNIQUES;

DYNAMICAL SYSTEMS;

EID: 68749086114     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.camwa.2009.06.040     Document Type: Article

References (26)

1. Shubin C. Singularly perturbed integral equations. J. Math. Anal. Appl. 313 (2006) 234-250
2. Kadalbajoo M.K., and Patidar K.C. A survey of numerical techniques for solving singularly-perturbed ordinary differential equations. Appl. Math. Comput. 130 (2002) 457-510
3. Tirmizi I.A., Fazal-i-Haq, and Siraj-ul-Islam. Non-polynomial spline solution of singularly perturbed boundary value problems. J. Comput. Appl. Math. 196 (2008) 6-16
4. Smith O.R. Singularly Perturbed Theory (1985), Cambridge University Press, New York
5. Alnasr M.H. Modified multilag methods for singularly perturbed Volterra integral equations. Int. J. Comput. Math. (2000) 221-233
6. Baker C.T.H. The Numerical Treatment of Integral Equations (1977), Clarendon Press, Oxford
7. Delves L.M., and Mohamed J.L. Computational Methods for Integral Equations (1985), Cambridge University Press
8. In: Delves L.M., and Walsh J. (Eds). Numerical Solution of Integral Equations (1974), Clarendon Press, Oxford
9. Ramm A.G. Dynamical systems method for solving nonlinear operator equations. Int. J. Appl. Math. Sci. 1 N1 (2004) 97-110
10. Ramm A.G. Dynamical systems method for solving operator equations. Commun. Nonlinear Sci. Numer. Simul. 9 N2 (2004) 383-402
11. Ramm A.G. Dynamical systems method (DSM) and nonlinear problems. In: Lopez-Gomez J. (Ed). In Spectral Theory and Nonlinear Analysis (2005), World Sci. Publishers, Singapore 201-228
12. Ramm A.G. Dynamical systems method (DSM) for nonlinear equations in Banach spaces. Nonlinear Sci. Numer. Simul. 11 N3 (2006) 306-310
13. Ramm A.G. Dynamical systems method (DSM) for unbounded operators. Proc. Amer. Math. Soc. 134 N4 (2006) 1059-1063
14. Ramm A.G. Ill-posed problems with unbounded operators. J. Math. Anal. Appl. 325 (2007) 490-495
15. Ramm A.G. Dynamical systems method (DSM) for selfadjoint operators. J. Math. Anal. Appl. 328 2 (2007) 1290-1296
16. Ramm A.G. On unbounded operators and applications. Appl. Math. Lett. 21 (2008) 377-382
17. Ramm A.G. Discrepancy principle for DSM II. Comm. Nonlin. Sci. Numer. Simul. 13 (2008) 1256-1263
18. Ramm A.G. Inverse Problems (2005), Springer-Verlag, New York
19. Ramm A.G. Dynamical Systems Method for Solving Operator Equations (2007), Elsevier, Amsterdam
20. Sweilam N.H. On the numerical solution for deconvolution problems with noise. Aust. J. Math. Anal. Appl. 4 2 (2007) 1-8
21. Sweilam N.H., and Nagy A.M. Numerical studies on dynamical system method for solving ill-posed problems with noise. Aust. J. Math. Anal. Appl. 4 1 (2007) 1-7
22. Hoang N.S., and Ramm A.G. Dynamical systems method for solving linear finite-rank operator equations. Ann. Polon. Math. 95 (2009) 77-93
23. Hoang N.S., and Ramm A.G. Solving ill-conditioned linear algebraic systems by the dynamical systems method (DSM). J. Inverse Problems Sci. Eng. 16 N5 (2008) 617-630
24. Groetsch C.W. The Theory of Tikhonov Regularization for Fredholm Equations of the First Kind. Research Notes in Mathematics vol. 105 (1984), Pitman, Boston
25. Tikhonov A.N., and Arsenin V.Y. Solutions of Ill Posed Problems (1977), Winston, Washington, DC
26. In: Tikhonov A.N., and Goncharsky V. (Eds). Ill Posed Problems in Natural Sciences (1987), Mir, Moscow