Previous |  Up |  Next


In this paper, the finite difference method is applied to a boundary value problem for the mildly non-linear ordinary differential equation of the fourth order. The existence of a unique solution of both the differential and the difference problem is proved and an $O(h^2)$ estimate of the discretization error and its first difference quotient is derived. Some numerical examples are given.
[1] Babuška I., Práger M., Vitásek E.: Numerical Processes in Differential Equations. Publishers of Technical Literature, Prague and Interscience Publishers, a Division of John Wiley & Sons, London - New York - Sydney 1966. MR 0223101
[2] Gary J.: Computing Eigenvalues of Ordinary Differential Equations by Finite Differences. Mathematics of Computation, 19, No 91, (1965), p. 365-379. DOI 10.1090/S0025-5718-1965-0179926-X | MR 0179926
[3] Хао-Шоу: Однородные разностные схемы для уравнения четвертого порядка с разрывными коэффициентами. Ж. вычисл. матем. и матем. физ., 3, № 5, (1963), р. 841-860. MR 0157491 | Zbl 1145.93303
[4] Lees M.: Discrete Methods for Nonlinear two-point Boundary Value Problems. Numerical Solution of Partial Differential Equations, (J. H. Bramble, editor), p. 59-72, New York, Academic Press, 1966. MR 0202323 | Zbl 0148.39206
[5] Marek I.: On Approximate Methods in Eigenvalue Problems. Čas. pro pěst. mat., 92 (1967), p. 89-104. MR 0211598 | Zbl 0167.13903
[6] Růžičková H.: Boundary Value Problems for Ordinary Differential Equations of the 4th Order. (Czech). (Unpublished), CSc Thesis, VUT Brno, 1971.
[7] Самарский А. А.: Априорные оценки для разностных уравнений. Ж. вычисл, матем. и мат. физ., 1, № 6, (1961), р. 972-1000. MR 0148238 | Zbl 1160.68305
[8] Zlámal M.: On Mildly Nonlinear Elliptic Boundary Value Problems. Information Processing 68, p. 179-182, North-Holland Publ. Соmр. - Amsterdam 1969. MR 0258296
[9] Zlámal M.: Discretization and Error Estimates for Boundary Value Problems of the Second Order. Estrato da Calcolo, Vol. 4, fasc. 3, (1967), p. 541 - 550. DOI 10.1007/BF02576039 | MR 0275691
Partner of
EuDML logo