Tirmizi, Ikram A.; Twizell, E. H.; Siraj-Ul-Islam A numerical method for third-order non-linear boundary-value problems in engineering. (English) Zbl 1065.65098 Int. J. Comput. Math. 82, No. 1, 103-109 (2005). Summary: A second-order method is developed for the numerical solution of a nonlinear, third-order, boundary-value problem. The method arises from a four-point recurrence relation involving exponential terms, these being replaced by Padé approximants. The convergence of the method is discussed. The method is tested on a sandwich beam problem to demonstrate its usefulness. Cited in 10 Documents MSC: 65L10 Numerical solution of boundary value problems involving ordinary differential equations 34B15 Nonlinear boundary value problems for ordinary differential equations 65L20 Stability and convergence of numerical methods for ordinary differential equations 34K10 Boundary value problems for functional-differential equations Keywords:numerical example; recurrence relation; Padé approximants; convergence; sandwich beam problem; nonlinear, third-order boundary-value problem PDF BibTeX XML Cite \textit{I. A. Tirmizi} et al., Int. J. Comput. Math. 82, No. 1, 103--109 (2005; Zbl 1065.65098) Full Text: DOI References: [1] Collatz L, The Numerical Treament of Differential Equations (1960) [2] Fox L, The Numerical Solution of Two-point Boundary-value Problems in Ordinary Differential Equations (1957) · Zbl 0077.11202 [3] DOI: 10.1016/0045-7825(86)90129-5 · doi:10.1016/0045-7825(86)90129-5 [4] DOI: 10.1098/rspa.1938.0037 · JFM 64.1452.01 · doi:10.1098/rspa.1938.0037 [5] Kriess H, Mathematics of Computation 26 pp 606– (1972) [6] DOI: 10.1016/0045-7825(88)90066-7 · Zbl 0619.65056 · doi:10.1016/0045-7825(88)90066-7 [7] Na TY, Computational Methods in Engineering Boundary Value Problems (1979) [8] Roberts SM, Two-Point Boundary Value Problems: Shooting Methods (1972) · Zbl 0239.65061 [9] Usmani RA, Journal of Mathematics and Physical Science 18 pp 365– (1984) [10] DOI: 10.1016/S0898-1221(01)00204-8 · Zbl 0983.65089 · doi:10.1016/S0898-1221(01)00204-8 [11] DOI: 10.1002/cnm.1630070409 · Zbl 0727.65069 · doi:10.1002/cnm.1630070409 [12] DOI: 10.1002/cnm.1640101110 · Zbl 0812.65074 · doi:10.1002/cnm.1640101110 [13] DOI: 10.1080/00207160108805085 · Zbl 1079.74664 · doi:10.1080/00207160108805085 [14] Agarwal RP, Boundary Value Problems for Higher Order Differential Equations (1986) [15] DOI: 10.1016/0022-0396(78)90120-1 · Zbl 0355.34006 · doi:10.1016/0022-0396(78)90120-1 [16] DOI: 10.1115/1.3422787 · Zbl 0241.73043 · doi:10.1115/1.3422787 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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.