an:01781819
Zbl 0999.65074
Liu, G. R.; Wu, T. Y.
Multipoint boundary value problems by differential quadrature method
EN
Math. Comput. Modelling 35, No. 1-2, 215-227 (2002).
00081731
2002
j
65L10 74K10 34B05 65L60 34B10 74S25
numerical examples; differential quadraturemethod; generalized collocation method; multipoint boundary value problem; shear deformation of sandwich beams; four-point nonlinear fourth-order systems
Summary: This paper extends the application of the differential quadrature method (DQM) to high order (\(\geq 3^{\text{rd}}\)) ordinary differential equations with the boundary conditions specified at multiple points (\(\geq\) 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 four-point 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.