Sentence examples for transform solution from inspiring English sources
From a transform solution, approximations are derived and analysed for several configurations.
First, an exact transform solution for the auxiliary problem of multiple-zone (integer n > 1) surface tractions is obtained.
We develop numerical data analysis procedures based upon the scattering transform solution to the KdV equation as given by Gardner et al. [ 1 ].
The proposed differential transform solution uses a set of mathematical operations to transform the heat conduction equation together with the fin profile in order to yield a closeform series of homogeneous extended surface heat diffusion equation.
All problems are treated analytically using bounded Green's functions for thin elastic plates, a discrete Fourier transform solution method and simple, explicit and rapidly convergent evaluations of the one- and two-dimensional lattice sums that arise.
It is shown that noncausal effects appearing in the first milliseconds of time signals with the use of discrete Fourier transforms are avoided with the Laplace transform solution method.
The system of governing equations is solved with the generalized Crank Nicholson method of central finite differences and approximate methods based on averaging certain process parameters, which use simple Laplace transform solutions for particular cases.
For these cases, high-resolution numerical integrations of the spectral transform model are used to provide reference solutions against which alternative numerical schemes and lower resolution spectral transform solutions can be evaluated.
Assuming the disturbances to be harmonically time dependent, the transformed solution is obtained in the frequency domain.
Numerical approximations to the Fourier transformed solution of partial differential equations are obtained via Monte Carlo simulation of certain random multiplicative cascades.
In the second part analytical solutions for the forced harmonic vibrations of the system are given and the transformed solution for mass impact is inverted numerically for large time.
