Abstract: Crosstalk among interconnects and printed-circuit
board (PCB) traces is a major limiting factor of signal quality in highspeed
digital and communication equipments especially when fast
data buses are involved. Such a bus is considered as a planar
multiconductor transmission line. This paper will demonstrate how
the finite difference time domain (FDTD) method provides an exact
solution of the transmission-line equations to analyze the near end
and the far end crosstalk. In addition, this study makes it possible to
analyze the rise time effect on the near and far end voltages of the
victim conductor. The paper also discusses a statistical analysis,
based upon a set of several simulations. Such analysis leads to a
better understanding of the phenomenon and yields useful
information.
Abstract: In this work we adopt a combination of Laplace
transform and the decomposition method to find numerical solutions
of a system of multi-pantograph equations. The procedure leads to a
rapid convergence of the series to the exact solution after computing a
few terms. The effectiveness of the method is demonstrated in some
examples by obtaining the exact solution and in others by computing
the absolute error which decreases as the number of terms of the series
increases.
Abstract: A method for solving linear and non-linear Goursat
problem is given by using the two-dimensional differential transform
method. The approximate solution of this problem is calculated in
the form of a series with easily computable terms and also the exact
solutions can be achieved by the known forms of the series solutions.
The method can easily be applied to many linear and non-linear
problems and is capable of reducing the size of computational work.
Several examples are given to demonstrate the reliability and the
performance of the presented method.