Sentence examples for integration rules from inspiring English sources

Review of integration rules, integrating rational functions, and improper integrals.

Some of the resultant integrals are evaluated by using the Gauss Chebyshev integration rules after moving the series coefficients to the outside of the integral sign; others are evaluated exactly, including the modified hypersingular integral.

The default integrators in Matlab (The MathWorks, Natick, MA) such as ode15s[ 21] employ similar integration rules and error estimates.

For smaller errors, high-order integration rules are more efficient.

Once the reduced integration rules are decided, the equivalent collocation form can be derived.

It is shown how the standard FFT method can be applied in combination with various numerical integration rules.

For this purpose, we apply the backward Euler method in addition to the product trapezoidal integration rule [19] for the integral term.

In order to cope with this problem we have modified the rendering algorithm so that it uses a different integration rule to solve the ray integral.

In this paper, a digital IIR integrator design based on the recursive Romberg integration rule and the fractional sample delay is investigated.

The three layers are discretized by using 8-node brick elements and integrals over elements are numerically evaluated by using a reduced Gauss integration rule.

Based on this fact, the conventional FOI is applied to design fixed Feller FOI including trapezoidal integration rule and Simpson integration rule methods.