Agarwal, Ravi P.; Chow, Y. M. Iterative methods for a fourth order boundary value problem. (English) Zbl 0541.65055 J. Comput. Appl. Math. 10, 203-217 (1984). Summary: We consider a fourth order nonlinear ordinary differential equation together with two-point boundary conditions and provide a-priori error estimates on the length of the interval (b-a) so that the Picard’s iterative method, the approximate Picard’s iterative method and the quasilinear iterative method converge to the solution of the problem. Cited in 78 Documents MSC: 65L10 Numerical solution of boundary value problems involving ordinary differential equations 34B15 Nonlinear boundary value problems for ordinary differential equations Keywords:fourth order differential equation; convergence; a-priori error estimates; Picard’s iterative method; quasilinear iterative method × Cite Format Result Cite Review PDF Full Text: DOI References: [1] Agarwal, R. P., The numerical solution of multipoint boundary value problems, J. Comput. Appl. Math., 5, 17-24 (1979) · Zbl 0394.65025 [2] Agarwal, R. P., On the periodic solutions of nonlinear second order differential systems, J. Comput. Appl. Math., 5, 117-123 (1979) · Zbl 0407.34021 [3] Agarwal, R. P., Method of complementary functions for nonlinear boundary value problems, J. Optim. Theory Appl., 36, 139-144 (1982) · Zbl 0448.34016 [4] Agarwal, R. P.; Akrivis, G., Boundary value problems occurring in plate deflection theory, J. Comput. Appl. Math., 8, 145-154 (1982) · Zbl 0503.73061 [5] Agarwal, R. P., Some inequalities for a function having \(n\) zeros, (Proc. Conf. ‘General Inequalities 3’. Proc. Conf. ‘General Inequalities 3’, Oberwolfach (1981)) · Zbl 0599.26037 [6] Agarwal, R. P., Boundary value problems for higher order integro-differential equations, Nonlinear Anal.: TMA, 7, 259-270 (1983) · Zbl 0505.45002 [7] R.P. Agarwal and S.L. Loi, On approximate Picard’s iterates for multipoint boundary value problems, Nonlinear Anal.: TMA; R.P. Agarwal and S.L. Loi, On approximate Picard’s iterates for multipoint boundary value problems, Nonlinear Anal.: TMA · Zbl 0567.65054 [8] Babuska, I.; Prager, M.; Vitasek, E., Numerical Processes in Differential Equations (1966), Wiley: Wiley New York · Zbl 0156.16003 [9] Bellman, R. E.; Kalaba, R. E., Quasilinearization and Nonlinear Boundary Value Problems (1965), Elsevier: Elsevier New York · Zbl 0139.10702 [10] Bernfeld, S. R.; Lakshmikantham, V., An Introduction to Nonlinear Boundary Value Problems (1974), Academic Press: Academic Press New York · Zbl 0286.34018 [11] Collatz, L., The Numerical Treatment of Differential Equations (1966), Springer: Springer New York · Zbl 0221.65088 [12] Keller, H. B., Numerical Methods for Two-Point Boundary Value Problems (1968), Ginn-Blaisdell: Ginn-Blaisdell Boston, MA · Zbl 0172.19503 [13] Lal, M.; Moffatt, D., Picard’s successive approximation for non-linear two-point boundary-value problems, J. Comput. Appl. Math., 8, 233-236 (1982) · Zbl 0494.65051 [14] Lee, E. S., Quasilinearization and Invariant Imbedding (1968), Academic Press: Academic Press New York · Zbl 0212.17602 [15] Na, T. Y., Computational Methods in Engineering Boundary Value Problems (1979), Academic Press: Academic Press New York · Zbl 0456.76002 [16] Rall, L. B., Computational Solutions of Nonlinear Operator Equations (1969), Wiley: Wiley New York · Zbl 0175.15804 [17] Reiss, E. L.; Callegari, A. J.; Ahluwalia, D. S., Ordinary Differential Equations with Applications (1976), Holt, Rinehart and Winston: Holt, Rinehart and Winston New York · Zbl 0334.34002 [18] J. Schröder, Fourth order two-point boundary value problems; estimates by two-sided bounds, Nonlinear Anal.: TMA; J. Schröder, Fourth order two-point boundary value problems; estimates by two-sided bounds, Nonlinear Anal.: TMA [19] Šeda, V., On a nonlinear boundary value problem, Acta Math. Univ. Comenian, XXX, 95-119 (1975) · Zbl 0318.34028 [20] Usmani, R. A., Discrete variable methods for a boundary value problem with engineering applications, Math. Comp., 32, 1087-1096 (1978) · Zbl 0387.65050 [21] Usmani, R. A.; Meek, D. S., On the application of a five-band matrix in the numerical solution of a boundary value problem, Utilitas Math., 14, 21-29 (1978) · Zbl 0388.65037 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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.