Generally, we omit the t-dependence of the integrands
in the notation.
In the course of these calculations, two rather complex integrals appear, involving integrands
which are trigonometric functions raised to fractional powers; however, we were able to evaluate them, and this allowed the determination of a valid first-order approximation to the solution, i.
The square brackets in the triple integrals in (2) indicate that the integrands
[[rho]/r"] and [[rho]u/r"] are to be integrated over the volume of the central object at the retarded time.
Moreover, since the integrands
involved in the foregoing sum are positive functions, then, for each index j = [bar.
This high quality of numerical integration is not surprising, given the smoothness of the integrands
in every dimension.
Among the topics are the abstract framework, co-observations, quadrature rules of interpolatory type, periodic integrands
, and problems.
However, for each of the one-forms [beta] and [gamma] the integrands
[rho]u x w * x and [rho]v x u * x vanish identically and one cannot apply the homotopy formula for their integration.
Since the integrands
in the above integrals above are monotone, we get
There are several methods used to deal with singular integrands
, and all are deterministic, adaptive strategies that will speed the convergence and integration process.
0,t]]) as the basic integrator process with integrands
restricted to a special class of exponential processes.
This expression cannot be simplified because the integrands
We used a quadrature scheme designed for integrands
of the form [(x-l).