zbMATH — the first resource for mathematics

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.

65L10 Numerical solution of boundary value problems involving ordinary differential equations
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), Dover New York · JFM 50.0554.12
[3] Timoshenko, S.P., Theory of elastic stability, (1961), McGrawCHill New York
[4] Soedel, W., Vibrations of shells and plates, (1993), Dekker New York · Zbl 0865.73002
[5] Dulacska, E., Soil settlement effects on buildings, ()
[6] Dahlquist, G.; Bjorck, A.; Anderson, N., Numerical methods, (1974), Prentice-Hall Englewood Cliffs, NJ
[7] Lund, J.; Bowers, K., Sinc methods for quadrature and differential equations, (1992), SIAM Philadelphia · 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^∗, 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, () · Zbl 0453.65053
[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.
[13] Keller, H.B., Numerical methods for two points boundary value problems, (1968), Blaisdell Pub. Co New York · Zbl 0172.19503
[14] Burden, R.L.; Faires, J.D., Numerical analysis, (1993), PWS Boston · Zbl 0788.65001
[15] Greenspan, D.; Casulli, V., Numerical analysis for applied mathematics, science, and engineering, (1998), Addison-Wesley
[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) · Zbl 0385.65038
[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, 2-3, 393-399, (2003) · Zbl 1034.47030
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.