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Multipoint boundary value problems by differential quadrature method

✍ Scribed by G.R. Liu; T.Y. Wu

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
997 KB
Volume
35
Category
Article
ISSN
0895-7177

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✦ Synopsis

This paper extends the application of the differential quadrature method (DQM) to high order (2 3rd) ordinary differential equations with the boundary conditions specified at multiple points (2 three different points). Explicit weighting coefficients for higher order derivatives have been derived using interpolating trigonometric polynomials. A three-point, linear third-order differential equation governing the shear deformation of sandwich beams is examined. Two examples of fourpoint nonlinear fourth-order systems are also presented. Accurate results are obtained for the example problems. Since boundary conditions are usually specified only at two extreme ends and not at intermediate boundary points, the present work opens new areas of application of the DQM.

πŸ“œ SIMILAR VOLUMES

Multipoint Boundary Value Problems for O
Multipoint Boundary Value Problems for Ordinary Differential Systems
✍ P.W. Eloe; J. Henderson πŸ“‚ Article πŸ“… 1994 πŸ› Elsevier Science 🌐 English βš– 292 KB

Solutions, \(u(x)\), of the first order system, \(u^{\prime}=f(x, u)\), satisfying the multipoint boundary conditions, \(\sum_{i=1}^{k} M_{i} u\left(x_{j}\right)=r\), are differentiated with respect to the components of \(r\) and with respect to the boundary points, \(x_{j}\), where \(M_{1}, \ldots,