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Approximation methods for nonlinear problems with application to two- point boundary value problems. (English) Zbl 0308.65039

MSC:
65J05 General theory of numerical analysis in abstract spaces
65L10 Numerical solution of boundary value problems involving ordinary differential equations
65J99 Numerical analysis in abstract spaces
34B15 Nonlinear boundary value problems for ordinary differential equations
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[1] Herbert B. Keller, Accurate difference methods for linear ordinary differential systems subject to linear constraints, SIAM J. Numer. Anal. 6 (1969), 8 – 30. · Zbl 0176.14801 · doi:10.1137/0706002 · doi.org
[2] Herbert B. Keller, Newton’s method under mild differentiability conditions, J. Comput. System Sci. 4 (1970), 15 – 28. · Zbl 0191.16001 · doi:10.1016/S0022-0000(70)80009-5 · doi.org
[3] Herbert B. Keller, Accurate difference methods for nonlinear two-point boundary value problems, SIAM J. Numer. Anal. 11 (1974), 305 – 320. · Zbl 0282.65065 · doi:10.1137/0711028 · doi.org
[4] H. B. Keller and A. B. White Jr., Difference methods for boundary value problems in ordinary differential equations, SIAM J. Numer. Anal. 12 (1975), no. 5, 791 – 802. · Zbl 0316.65017 · doi:10.1137/0712059 · doi.org
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[8] R. B. Simpson, Existence and error estimates for solutions of a discrete analog of nonlinear eigenvalue problems, Math. Comp. 26 (1972), 359 – 375. · Zbl 0256.65048
[9] Hans J. Stetter, Asymptotic expansions for the error of discretization algorithms for non-linear functional equations, Numer. Math. 7 (1965), 18 – 31. · Zbl 0148.39003 · doi:10.1007/BF01397970 · doi.org
[10] Hans J. Stetter, Stability of nonlinear discretization algorithms, Numerical Solution of Partial Differential Equations (Proc. Sympos. Univ. Maryland, 1965) Academic Press, New York, 1966, pp. 111 – 123.
[11] Richard Weiss, The application of implicit Runge-Kutta and collection methods to boundary-value problems, Math. Comp. 28 (1974), 449 – 464. · Zbl 0284.65067
[12] A. B. WHITE, Numerical Solution of Two Point Boundary Value Problems, Ph. D. Thesis, Calif. Inst. of Technology, Pasadena, 1974.
[13] Victor Pereyra, Iterated deferred corrections for nonlinear operator equations, Numer. Math. 10 (1967), 316 – 323. · Zbl 0258.65059 · doi:10.1007/BF02162030 · doi.org
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