Abstract
We made a new A-stable 3-stage fourth order Runge-Kutta formula which can be calculated in parallel. Our matrix A, whose components identify an IRK formula together with the vector b, and its eigenvalues can be expressed in a closed algebraic form. The diagonalization of A is a crucial point for our parallel algorithm. The eigenvalues of A should be greater than 1/2 for the A_0-stability. However we find that the smaller the eigenvalue of A is, the more accurate the solution of the parallelized IRK is.
