The paper improves a preliminary experimental study on a cluster by adding both theoretical results and experimental tests on a grid platform. These algorithms solve univalued and multivalued pseudo-linear problems using parallel asynchronous multisplitting methods combined with Krylov’s methods. This paper also analyses these algorithms using contraction techniques. Two distinct applications, with discretized boundary value problems, are analyzed and simulated. First, a univalued convection-diffusion problem perturbed by an increasing diagonal operator is presented. Then, follows the description of a diffusion problem whose solution is constrained. This situation classically leads to the solution of a multivalued pseudo-linear problem in which the linear part is perturbed by an increasing diagonal multivalued operator. Parallel asynchronous and synchronous algorithms were implemented and tested on a grid platform composed of physically adjacent or geographically distant machines. In addition, the simulation results are detailed and show that the elapsed times obtained for the asynchronous algorithms are significantly less than those obtained for the synchronous algorithms.