# Asynchronous Communications Library for the Parallel-in-Time Solution of Black-Scholes Equation

## TL;DR

This paper presents an implementation of asynchronous parallel algorithms for solving the Black-Scholes equation, demonstrating improved efficiency and resource management through the use of the JACK2 library.

## Contribution

It introduces an implementation of asynchronous parareal algorithms using JACK2, addressing resource management and convergence detection challenges.

## Key findings

- Asynchronous algorithms improve computational efficiency.
- JACK2 effectively manages resources in parallel computations.
- Experimental results confirm the method's effectiveness.

## Abstract

The advent of asynchronous iterative scheme gives high efficiency to numerical computations. However, it is generally difficult to handle the problems of resource management and convergence detection. This paper uses JACK2, an asynchronous communication kernel library for iterative algorithms, to implement both classical and asynchronous parareal algorithms, especially the latter. We illustrate the measures whereby one can tackle the problems above elegantly for the time-dependent case. Finally, experiments are presented to prove the availability and efficiency of such application.