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The numerical solution of boundary value problems for second order functional differential equations by finite differences. (English) Zbl 0247.65053


MSC:

65L10 Numerical solution of boundary value problems involving ordinary differential equations
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[1] Ciarlet, P. G., Schultz, M. H., Varga, R. S.: Numerical methods of high order accuracy for nonlinear boundary value problems. V. Monotone operator theory. Numer. Math.13, 51-77 (1969). · Zbl 0181.18603 · doi:10.1007/BF02165273
[2] Cryer, C. W.: The numerical solution of boundary value problems for second order functional differential equations by finite differences. Technical Report #127, Computer Sciences Dept., University of Wisconsin, Madison, Wisconsin, 1971. · Zbl 0212.44002
[3] Cryer, C. W.: TheLU-factorization of totally positive matrices. Linear Algebra and Its Applications, to appear. · Zbl 0274.15004
[4] Cryer, C. W., Tavernini, L.: The numerical solution of Volterra functional differential equations by Euler’s method. SIAM J. Numer. Anal.9, 105-129 (1972). · Zbl 0244.65085 · doi:10.1137/0709012
[5] Fennell, R., Waltman, P.: Boundary value problems for functional differential equations. Bull. Amer. Math. Soc.75, 487-489 (1969). · Zbl 0211.17901 · doi:10.1090/S0002-9904-1969-12211-1
[6] Fennell, R., Waltman, P.: A boundary value problem for a system of nonlinear functional differential equations. J. Math. Anal. Appl.26, 447-453 (1969). · Zbl 0172.12103 · doi:10.1016/0022-247X(69)90167-X
[7] Fischer, C. F., Usmani, R. A.: Properties of some tridiagonal matrices and their application to boundary value problems. SIAM J. Numer. Anal.6, 127-142 (1969). · Zbl 0176.46802 · doi:10.1137/0706014
[8] Gantmacher, F. R.: The theory of matrices, vol. I. New York: Chelsea 1959. · Zbl 0085.01001
[9] Gantmacher, F. R., Krein, M. G.: Oszillationsmatrizen, Oszillationskerne und kleine Schwingungen mechanischer Systeme. Berlin: Akademie 1960. · Zbl 0088.25103
[10] Grimm, L. J., Schmitt, K.: Boundary value problems for delay-differential equations. Bull. Amer. Math. Soc.74, 997-1000 (1968). · Zbl 0167.38504 · doi:10.1090/S0002-9904-1968-12114-7
[11] Grimm, L. J., Schmitt, K.: Boundary value problems for differential equations with deviating arguments. Aequationes Math.4, 176-190 (1970). · Zbl 0198.13201 · doi:10.1007/BF01817758
[12] Halanay, A.: On a boundary value problem for linear systems with time lag. J. Differential Equ.2, 47-56 (1966). · Zbl 0142.06104 · doi:10.1016/0022-0396(66)90062-3
[13] Halanay, A., Yorke, J. A.: Some new results and problems in the theory of differential-delay equations. SIAM Review13, 55-80 (1971). · Zbl 0216.11902 · doi:10.1137/1013004
[14] Hale, J. K.: Functional differential equations. New York: Springer 1971. · Zbl 0222.34003
[15] Henrici, P.: Discrete variable methods in ordinary differential equations. New York: Wiley 1962. · Zbl 0112.34901
[16] Kato, S.: Asymptotic behavior in functional differential equations. Tohoku Math. J.18, 174-215 (1966). · Zbl 0154.08901 · doi:10.2748/tmj/1178243447
[17] Keller, H. B.: Numerical methods for two-point boundary-value problems. Waltham, Mass.: Blaisdell 1968. · Zbl 0172.19503
[18] Nevers, K. de, Schmitt, K.: An application of the shooting method to boundary value problems for second order delay equations. J. Math. Anal. Appl.36, 588-597 (1971). · Zbl 0219.34050 · doi:10.1016/0022-247X(71)90041-2
[19] Norkin, S. B.: Differential equations of second order with deviating arguments. Providence: Amer. Math. Soc. 1972. · Zbl 0234.34080
[20] Ortega, J. M., Rheinboldt, W. C.: Iterative solution of nonlinear equations in several variables. New York: Academic Press 1970. · Zbl 0241.65046
[21] Schmitt, K.: Comparison theorems for second order delay-differential equations. Rocky Mountain Math. J.1, 459-467 (1971). · Zbl 0226.34063 · doi:10.1216/RMJ-1971-1-3-459
[22] Tavernini, L.: One-step methods for the numerical solution of Volterra functional differential equations. SIAM J. Numer. Anal.8, 766-795 (1971). · Zbl 0231.65070 · doi:10.1137/0708072
[23] Tavernini, L.: Linear multistep methods for the numerical solution of Volterra functional differential equations. Applicable Anal., to appear. · Zbl 0291.65020
[24] Tavernini, L.: Numerical methods for Volterra functional differential equations. Invited paper, SIAM Fall Meeting, October 1971, Madison, Wisconsin. · Zbl 0231.65070
[25] Tavernini, L.: Quadratic and cubic spline approximations for Volterra functional differential equations. Manuscript. · Zbl 0291.65020
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