We present recent results on naturally parallelizable
numerical methods for solving time-dependent PDEs by the
Fourier-Laplace transformation. Unlikely to the standard
time-marching methods, we apply the Fourier-Laplace transformation
in time to time-dependent PDEs, solve the resulting
space-frequency domain problems in parallel. Then using the
inverse transformation, we recover the time-domain solutions.

In particular, the usual time-marching algorithms for
integro-differential equations with memory term require the huge
storage to store all the previous time-step solutions and
numerical integrations to advance to the next time step.
However, our transformation method applied to these problems
does not need these expensive storages and calculations;
moreover it is naturally parallelizable.