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Uniform difference method for a parameterized singular perturbation problem. (English) Zbl 1096.65069
Authors’ summary: We consider a uniform finite difference method on a B-mesh is applied to solve a singularly perturbed quasilinear boundary value problem (BVP) depending on a parameter. We give a uniform first-order error estimates in a discrete maximum norm. Numerical results are presented that demonstrate the sharpness of our theoretical analysis.

65L10Boundary value problems for ODE (numerical methods)
65L12Finite difference methods for ODE (numerical methods)
Full Text: DOI
[1] Zawischa, K.: Uber die differentialgleichung deren losungskurve durch zwei gegebene punkte hindurchgehen soll. Monatsh. math. Phys. 37, 103-124 (1930) · Zbl 56.1048.02
[2] Pomentale, T.: A constructive theorem of existence and uniqueness for problem y’=f(x,y,${\lambda}), y(a)={\alpha}, y(b)={\beta}$. Z. angew. Math. mech. 56, 387-388 (1976) · Zbl 0338.34019
[3] Feckan, M.: Parametrized singularly perturbed boundary value problems. J. math. Anal. appl. 188, 426-435 (1994) · Zbl 0812.34020
[4] Jankowski, T.: Monotone iterations for differential problems. Math. notes, miscolc 2, 31-38 (2001) · Zbl 1002.34009
[5] Jankowski, T.; Lakshmikantham, V.: Monotone iterations for differential equations with a parameter. J. appl. Math. stoch. Anal. 10, 273-278 (1997) · Zbl 0992.34010
[6] Ronto, M.; Csikos-Marinets, T.: On the investigation of some non-linear boundary value problems with parameters. Math. notes, miscolc 1, 157-166 (2000) · Zbl 0973.34013
[7] Stanek, S.: Nonlinear boundary value problem for second order differential equations depending on a parameter. Math. slovaca 47, 439-449 (1997) · Zbl 0964.34013
[8] Gulle, A.; Duru, H.: Convergence of the iterative process to the solution of the boundary problem with the parameter. Trans. acad. Sci. azerb., ser. Phys. tech. Math. sci. 18, 34-40 (1998) · Zbl 1203.65114
[9] O’malley, R. E.: Singular perturbations methods for ordinary differential equations. (1991)
[10] Nayfeh, A. H.: Introduction to perturbation techniques. (1993) · Zbl 0449.34001
[11] Doolan, E. R.; Miller, J. J. H.; Schilders, W. H. A.: Uniform numerical methods for problems with initial and boundary layers. (1980) · Zbl 0459.65058
[12] Farrell, P. A.; Hegarty, A. F.; Miller, J. J. H.; O’riordan, E.; Shishkin, G. I.: Robust computational techniques for boundary layers. (2000) · Zbl 0964.65083
[13] Roos, H. G.; Stynes, M.; Tobiska, L.: Numerical methods for singularly perturbed differential equations. Springer series in computational mathematics 24 (1996) · Zbl 0844.65075
[14] Amiraliyev, G. M.: Difference method for the solution one problem of the theory dispersive waves. USSR diff. Equat. 26, 2146-2154 (1990)
[15] Amiraliyev, G. M.; Duru, H.: A uniformly convergent finite difference method for a singularly perturbed initial value problem. Appl. math. Mech. (English edition) 20, 379-387 (1999) · Zbl 0977.65060
[16] Amiraliyev, G. M.; Duru, H.: A uniformly convergent difference method for the periodical boundary value problem. Comput. math. Appl. 46, 695-703 (2003) · Zbl 1054.65080
[17] Boglaev, I. P.: Approximate solution of a non-linear boundary value problem with a small parameter for the highest order derivative. USSR comput. Math. math. Phys. 24, 30-39 (1984) · Zbl 0595.65093
[18] Amiraliyev, G. M.: On the numerical solution of the system of boussinusque with boundary layers. USSR model. Mech. 3, No. 5, 3-14 (1988)