Sentence examples for transform the solution from inspiring English sources

By applying an integral transform, the solution is obtained in the form of single integral and then an approximate form of the solution is derived.

By means of space and time Fourier transform, the solution is reduced to a set of fundamental solutions which are related to different symmetries.

By the Laplace transform, Lemma 2.2, and the inverse Laplace transform, the solution of (2.4) is given as T_{n}(t)=E_{alpha,1}bigl -lambda_{n}t^{alpha} bigr).

A numerical mapping technique is evoked to transform the solution domain into a rectangular geometry and the procedure is used to solve for frequencies where cross modes can propagate in the straight sections of duct.

Within a single formula derived by using the Laplace transform and inverse transform, the solution covers the contributions of the external excitations, the nonzero initial conditions and the inhomogeneous boundary conditions altogether, including such boundary conditions that the dependent variables at the ends of the rod are restricted with an equation.

Then inverse transform the solutions of the algebraic equations, the Green's functions can be expressed by contour integral.

Second, the discrete dimensional-convolution procedure, which transforms the solution to the non-recursive expression of n, including a finite number of elementary operations and functions.

The Laplace transform inversion integral transforms the solution from the complex domain to the time domain by use of the residue theorem.

The process of transforming the solution to vapour is usually activated by the act of inhaling through, or 'vaping', the device (Dawkins, Turner, Roberts, & Soar, 2013).

It follows from Gronwall's lemma that sup t ∈ [ 0, T Z Z ( t ) < ∞, which implies that S t is a continuous semigroup by the standard O.D.E. theory. □. We transform the global solution of the equivalent system (2.10) into the global conservative solution of the original system (2.1) in this section.

By combining the methods of separation of variables and the Laplace transform, the exact solution of the DPL model of heat conduction in a three-dimensional bounded domain has been obtained and analyzed.