Application of the generalized differential quadrature rule to eighth‐order differential equations
Copyright policy )Application of the generalized differential quadrature rule to eighth‐order differential equations
AbstractThis work extends the application of the generalized differential quadrature rule (GDQR) to an eighth‐order boundary‐value differential equation with four boundary conditions at boundaries. The differential quadrature expression and explicit weighting coefficients for the eighth‐order differential equation are formulated for a first time to implement the GDQR more accurately. A circular cylindrical single‐barrel roof is employed as an example. The numerical results show good accuracy and convergence with only a few sampling points. The application of the GDQR is straightforward and has clear advantages in the implementation of multiple boundary conditions over the existing δ‐point technique. The GDQR has demonstrated itself as a general numerical method to solve high‐order differential equation with multiple boundary conditions. Copyright © 2001 John Wiley & Sons, Ltd.
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Numerical solution of boundary value problems involving ordinary differential equations, convergence, Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations, pseudospectral method, Pseudospectral method, Shell structure, Generalized differential quadrature rule, 510, 620, generalized differential quadrature rule, collocation method, Differential quadrature method, Linear boundary value problems for ordinary differential equations, Numerical methods, Stability and convergence of numerical methods for ordinary differential equations, Collocation method, differential quadrature method
Numerical solution of boundary value problems involving ordinary differential equations, convergence, Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations, pseudospectral method, Pseudospectral method, Shell structure, Generalized differential quadrature rule, 510, 620, generalized differential quadrature rule, collocation method, Differential quadrature method, Linear boundary value problems for ordinary differential equations, Numerical methods, Stability and convergence of numerical methods for ordinary differential equations, Collocation method, differential quadrature method
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