Multipoint boundary value problems by differential quadrature method

Abstract

This paper extends the application of the differential quadrature method (DQM) to high order (≥ 3rd) ordinary differential equations with the boundary conditions specified at multiple points (≥ 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. © 2001 Elsevier Science Ltd. All rights reserved.