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An efficient computational method for second order boundary value problems of nonlinear differential equations. (English) Zbl 1193.65134
Summary: We will discuss a class of boundary value problems (BVPs) of nonlinear differential equations in the reproducing kernel space. The existence of the solution and a iterative method are established for the kind of problems. Some examples are displayed to demonstrate the computation efficiency of the method.

65L10Boundary value problems for ODE (numerical methods)
Full Text: DOI
[1] A.E.H. Love, A Treatise on the Mathematical Theory of Elasticity, fourth ed., New York, 1944.
[2] Prescott, J.: Applied elasticity. (1961) · Zbl 50.0554.12
[3] Timoshenko, S. P.: Theory of elastic stability. (1961)
[4] Soedel, W.: Vibrations of shells and plates. (1993) · Zbl 0865.73002
[5] Dulacska, E.: Soil settlement effects on buildings. Developments in geotechnical engineering 69 (1992)
[6] Dahlquist, G.; Bjorck, A.; Anderson, N.: Numerical methods. (1974)
[7] Lund, J.; Bowers, K.: Sinc methods for quadrature and differential equations. (1992) · Zbl 0753.65081
[8] Michael, K.: Fast iterative methods for symmetric sinc -- Galerkin system. SIAM J. Numer. anal. 19, 357-373 (1999) · Zbl 0952.65057
[9] Scott, M. R.; Watts, H. A.: Computational solution of linear two-point boundary value problems via orthonormalization. SIAM J. Numer. anal. 14, 40-70 (1977) · Zbl 0357.65058
[10] Watson, Layne T.; Scott, Melvin R.: Solving spline-collocation approximations to nonlinear two-point boundary-value problems by a homotopy method$\ast $. Appl. math. Comput. 24, 333-357 (1987) · Zbl 0635.65099
[11] Scott, M. R.; Watts, H. A.: A systematized collection of codes for solving two-point boundary-value problems. Numerical methods for differential systems (1976)
[12] M.R. Scott, H.A. Watts, Computational Solution of Nonlinear Two-Point Boundary-Value Problems, in: Proceedings of the 5th symposium Computers in Chemical Engineering, 1977, pp. 17 -- 28. · Zbl 0357.65058
[13] Keller, H. B.: Numerical methods for two points boundary value problems. (1968) · Zbl 0172.19503
[14] Burden, R. L.; Faires, J. D.: Numerical analysis. (1993) · Zbl 0788.65001
[15] Greenspan, D.; Casulli, V.: Numerical analysis for applied mathematics, science, and engineering. (1998) · Zbl 0658.65001
[16] Chwla, M. M.: A fourth order tri-diagonal finite difference method for general non-linear two point boundary value problems with mixed boundary conditions. J. inst. Math. appl. 21, 83-93 (1978)
[17] Chawla, M. M.: A sixth order tri-diagonal finite difference method for general non-linear two point boundary value problems with mixed boundary conditions. J. inst. Math. appl. 24, 35-42 (1979) · Zbl 0485.65055
[18] Mohanty, R. K.; Evans, D. J.; Dey, S.: Three points discretization of order four and six for (du/dx) of the solution of non-linear singular two point boundary value problems. Int. J. Comput. math. 78, 123-139 (2001) · Zbl 0984.65075
[19] Jain, M. K.; Iyengar, S. R. K.; Subramanyam, G. S.: Variable mesh methods for the numerical solution of two point singular pertubation problems. Comput. methods appl. Mech. eng. 42, 273-286 (1984) · Zbl 0514.65065
[20] Ha, S. N.: A nonlinear shooting method for two-point boundary value problems. Comput. math. Appl. 42, 1411-1420 (2001) · Zbl 0999.65077
[21] Mohanty, R. K.: A family of variable mesh methods for the estimates of (du/dr) and solution of non-linear two point boundary value problems with singularity. J. comput. Appl. math. 182, 173-187 (2005) · Zbl 1071.65113
[22] Li, Chunli; Cui, Minggen: The exact solution for solving a class of nonlinear operator equation in the reproducing kernel space. Appl. math. Comput. 143, No. 2 -- 3, 393-399 (2003) · Zbl 1034.47030