Numerical analysis: mathematics of scientific computing
Numerical analysis: mathematics of scientific computing
Elementary Numerical Analysis: An Algorithmic Approach
Elementary Numerical Analysis: An Algorithmic Approach
A note on the numerical solution of high-order differential equations
Journal of Computational and Applied Mathematics
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The differential quadrature method (DQM) is used to solve the first-order initial value problem. The initial condition is given at the beginning of the interval. The derivative of a space-independent variable at a sampling grid point within the interval can be defined as a weighted linear sum of the given initial conditions and the function values at the sampling grid points within the defined interval. Hermite polynomials have advantages compared with Lagrange and Chebyshev polynomials, and so, unlike other work, they are chosen as weight functions in the DQM. The proposed method is applied to a numerical example and it is shown that the accuracy of the quadrature solution obtained using the proposed sampling grid points is better than solutions obtained with the commonly used Chebyshev-Gauss-Lobatto sampling grid points.