The Sinc-Galerkin method for fourth-order differential equations
SIAM Journal on Numerical Analysis
Sinc methods for quadrature and differential equations
Sinc methods for quadrature and differential equations
The double-exponential transformation in numerical analysis
Journal of Computational and Applied Mathematics - Special issue on numerical analysis 2000 Vol. V: quadrature and orthogonal polynomials
Homotopy perturbation method: a new nonlinear analytical technique
Applied Mathematics and Computation
Double exponential formulas for numerical indefinite integration
Journal of Computational and Applied Mathematics
Recent developments of the Sinc numerical methods
Journal of Computational and Applied Mathematics - Special Issue: Proceedings of the 10th international congress on computational and applied mathematics (ICCAM-2002)
Journal of Computational and Applied Mathematics
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Journal of Computational and Applied Mathematics
Journal of Computational Physics
Sinc-Galerkin method for solving nonlinear boundary-value problems
Computers & Mathematics with Applications
Proof of Stenger's conjecture on matrix I( -1) of Sinc methods
Journal of Computational and Applied Mathematics
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Sinc approximate methods are often used to solve complex boundary value problems such as problems on unbounded domains or problems with endpoint singularities. A recent implementation of the Sinc method [Li, C. and Wu, X., Numerical solution of differential equations using Sinc method based on the interpolation of the highest derivatives, Applied Mathematical Modeling 31 (1) 2007 1-9] in which Sinc basis functions are used to approximate the highest derivative in the governing equation of the boundary value problem is evaluated for structural mechanics applications in which interlaminar stresses are desired. We suggest an alternative approach for specifying the boundary conditions, and we compare the numerical results for analysis of a laminated composite Timoshenko beam, implementing both Li and Wu's approach and our alternative approach for applying the boundary conditions. For the Timoshenko beam problem, we obtain accurate results using both approaches, including transverse shear stress by integration of the 3D equilibrium equations of elasticity. The beam results indicate our approach is less dependent on the selection of the Sinc mesh size than Li and Wu's SIHD. We also apply SIHD to analyze a classical laminated composite plate. For the plate example, we experience difficulty in obtaining a complete system of equations using Li and Wu's approach. For our approach, we suggest that additional necessary information may be obtained by applying the derivatives of the boundary conditions on each edge. Using this technique, we obtain accurate results for deflection and stresses, including interlaminar stresses by integration of the 3D equilibrium equations of elasticity. Our results for both the beam and the plate problems indicate that this approach is easily implemented, has a high level of accuracy, and good convergence properties.