Sentence examples for an integrating factor from inspiring English sources

Note that the solution to the stochastic Marmarou model is found through an "integrating factor" which involves an integration constant, the evaluation of which necessitates a unit of 1/min unit for the 2 inside the exponent of the exponential function.

Then (I t,x,dot{x})) is a first integral, and (mu t,x,dot {x})=I_{dot{x}}) is an integrating factor of the given second-order equation.  .

Then (I t,x,dot{x})) is a first integral, and (mu t,x,dot {x})=I_{dot{x}}) is an integrating factor of the given second-order equation.

If equation (1.1) has the first integral of the form (I=A t,x dot{x}+B t,x)), then equation (1.1) has an integrating factor of the form (mu =A t,x)).

then we say that μ(x) is an integrating factor of the Equation (1) (see [7]).

then we say that μ x, t) is an integrating factor of the partial differential equation (1.1).

Moreover, the integrability of a class of systems (quasidegenerate infinity systems) which generalize the so-called degenerate infinity vector fields is considered, and a method how to obtain an inverse integrating factor of the systems from the first integrals of the corresponding quasihomogeneous systems is shown.

By solving the systems of ordinary differential equations which are established by using the vector fields of the quasihomogeneous systems, one can obtain an inverse integrating factor of the systems.

Next, we turn to present a non-zero integrating factor ℑ(Y i (t), t) that can make equation in (61) an exact form by multiplying it on both sides of (61).

Fortunately, Yirong Liu and Jibin Li [21] found that there always exists a formal inverse integrating factor for three-order nilpotent critical points in 2009, and they gave a new definition of the focal values under the generalized triangle polar coordinates and the method of commuting Lyapunov constants using the inverse integral factors for the three-order nilpotent critical point.

The integrating factor (IF) method for numerical integration of stiff nonlinear PDEs has the disadvantage of producing large error coefficients when the linear term has large norm.