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Cubic spline solution of two-point boundary value problems with significant first derivatives. (English) Zbl 0497.65046


MSC:

65L10 Numerical solution of boundary value problems involving ordinary differential equations
65L60 Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations
34B15 Nonlinear boundary value problems for ordinary differential equations
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[1] Keller, H.B., Numerical methods for two-point boundary value problems, (1968), Ginn-Blaisdell New York · Zbl 0172.19503
[2] Allen, B.T., A new method for solving second order differential equations when the first derivative is present, Comp. J., 8, 392-394, (1965) · Zbl 0133.38304
[3] Stepleman, R.S., Tridiagonal fourth order approximations to general two-point nonlinear boundary value problems with mixed boundary conditions, Math. comp., 30, 92-103, (1976) · Zbl 0331.65048
[4] Chawla, M.M., A fourth-order tridiagonal finite difference method for general nonlinear two-point boundary value problems with mixed boundary conditions, J. inst. math. appl., 21, 83-93, (1978) · Zbl 0385.65038
[5] Chawla, M.M., A sixth-order tridiagonal finite difference method for general nonlinear two-point boundary value problems, J. inst. math. appl., 24, 35-42, (1979) · Zbl 0485.65055
[6] Albasiny, E.L.; Hoskins, W.D., Cubic spline solutions to two-point boundary value problems, Comp. J., 12, 151-153, (1969) · Zbl 0185.41403
[7] Ablasiny, E.L.; Hoskins, W.D., Increased accuracy cubic spline solutions to two-point boundary value problems, J. inst. math. appl., 9, 47-55, (1972) · Zbl 0243.65050
[8] Bickley, W.G., Piecewise cubic interpolation and two point boundary value problems, Comp. J., 11, 206-208, (1968) · Zbl 0155.48004
[9] Fyfe, D.J., The use of cubic splines in the solution of two-point boundary value problems, Comp. J., 12, 188-192, (1969) · Zbl 0185.41404
[10] Sakai, M., Piecewise cubic interpolation and two-point boundary value problems, Publ. res. inst. math. sci., 7, 345-362, (1971) · Zbl 0236.65054
[11] Sakai, M., Numerical solution of boundary value problems for second order functional differential equations by the use of cubic splines, Mem. fac. sci. kyushu univ., 29, 113-122, (1975) · Zbl 0318.65039
[12] Rubin, S.G.; Graves, R.A., Viscous flow solutions with a cubic spline approximation, Comput. & fluids, 3, 1-36, (1975) · Zbl 0347.76020
[13] Rubin, S.G.; Khosla, P.K., Higher order numerical solution using cubic splines, Aiaa j., 14, 851-858, (1976) · Zbl 0344.65048
[14] Tewarson, R.P., On the use of splines for the numerical solution of nonlinear two-point boundary value problems, Bit, 20, 223-232, (1980) · Zbl 0427.65060
[15] Ahlberg, J.H.; Nilson, E.N.; Walsh, J.L., The theory of splines and their applications, (1967), Academic Press New York · Zbl 0158.15901
[16] Greville, T.N.E., Theory and application of spline functions, (1969), Academic Press New York · Zbl 0215.17601
[17] Prenter, P.M., Splines and variational methods, (1975), Wiley New York · Zbl 0344.65044
[18] Mitchell, A.R.; Griffiths, D.F., Upwinding by Petrov-Galerkin methods in convection-diffusion problems, J. comput. appl. math., 6, 219-228, (1980) · Zbl 0467.76081
[19] Hemker, P.W.; Miller, J.J.H., Numerical analysis of singular perturbation problems, (1979), Academic Press New York · Zbl 0407.00011
[20] II’in, A.M., Differencing scheme for a differential equation with a small parameter affecting the highest derivatives, Math. notes, 6, 596-602, (1969) · Zbl 0191.16904
[21] Roscoe, D.F., New methods for the derivation of stable difference representations for differential equations, J. inst. math. appl., 16, 291-301, (1975) · Zbl 0327.65071
[22] Spalding, D.B., A novel finite difference formulation for differential expressions involving both first and second derivatives, Internat. J. numer. meths. engrg., 4, 551-559, (1972)
[23] Stoyan, G., Monotone difference schemes for diffusion-convection problems, Z. angew. math. mech., 59, 361-372, (1979) · Zbl 0484.65056
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