Parareal is a well-studied algorithm for numerically integrating systems of time-dependent differential equations by parallelising the temporal domain. Given approximate initial values at each sub-interval, locates solution in fixed number iterations using predictor-corrector, stopping once tolerance met. This iterative process combines solutions located inexpensive (coarse resolution) and expe...

in this paper, a new enhanced version of the particle swarm optimization (pso) is presented. an important modification is made by adding probabilistic functions into pso, and it is named probabilistic particle swarm optimization (ppso). since the variation of the velocity of particles in pso constitutes its search engine, it should provide two phases of optimization process which are: explorati...