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Zbl 1065.65098
Tirmizi, Ikram A.; Twizell, E.H.; Siraj-Ul-Islam
A numerical method for third-order non-linear boundary-value problems in engineering. (English)
[J] Int. J. Comput. Math. 82, No. 1, 103-109 (2005). ISSN 0020-7160; ISSN 1029-0265/e

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.

MSC 2000:: *65L10 Boundary value problems for ODE (numerical methods)
34B15 Nonlinear boundary value problems of ODE
65L20 Stability of numerical methods for ODE
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

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Zentralblatt MATH Berlin [Germany]