  Smoothed particle hydrodynamics (SPH) discretization techniques are
generalized to develop a method, smoothed particle interpolation (SPI), for
solving initial value problems of systems of non-hydrodynamical nature. Under
this approach, SPH is viewed as strictly an interpolation scheme and, as such,
suitable for solving general hyperbolic and parabolic equations. The SPI method
is tested on (1) the wave equation with inhomogeneous sound speed and (2)
Burgers equation. The efficiency of SPI is studied by comparing SPI solutions
to those obtained with standard finite difference methods. It is shown that the
power of SPI arises when the smoothing particles are free to move.
