| Description |
iv, 120 leaves : illustrations ; 29 cm |
| Summary |
"When integrating numerically, if the integrand can be expressed exactly as a polynomial of degree n, over a finite interval; then either Simpson's rule, Romberg integration, Legendre-Gauss or Jacobi-Gauss quadrature formulas provide good results. However, if the integrand can not be expressed exactly as an nth degree polynomial, then perhaps it can be expressed as a function f(x) divided by [square root]1-x² or as a function g(x) times (1-x)[superscript [alpha]] (l+x)[superscript [Beta]], where [alpha] and [Beta] are some real numbers -1, or as a function h(x) times one. If this is the case then the Chebyshev-Gauss, Jacobi-Gauss, and Legendre- Gauss quadrature are respectively quite useful. If the integrand can not be expressed as f(x)/[square root]1 -x² or as g(x)·(1-x)[superscript [alpha]]· (1+x)[superscript [Beta]] or as h(x) ·(1) then the Romberg method should be used. If the interval of integration is [0,[infinity]] or [-[infinity],[infinity]] then the Laguerre-Gauss and the Hermite-Gauss methods respectively are generally quite useful. The results of this study indicate that the quadrature formula to use in a given situation is dependent upon the interval of integration and the integrand. However, the results also indicate certain guide lines for choosing the type of quadrature formula to use in a given situation"--Abstract, leaf iii. |
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