1. A method for finding an approximation of a Hamilton-Jacobi equation using a parallel computing system, comprising: under control of one or more computer systems configured with a processor and a memory; providing a representation of an equation solution on a grid using data values represented on grid nodes; creating an active list using a subset of grid nodes, whose data values are configured to be updated simultaneously using an individual computing device for each grid node; computing a sequence of convergence solutions for the nodes in the active list that iteratively decrease the approximation error of the solution; updating the value of each grid node in the active list for each computation iteration using dependent data values of grid nodes from the previous iteration that are nearby in the grid; expanding the active list of grid nodes during each computation iteration to include all nodes that are influenced by the updates to data values from the current iteration; removing nodes from the active list whose values have reached an acceptable level of approximation error after an update; and creating a sequence of successively better approximations by modifying the active list and updating the active nodes until the active list is empty and all nodes on the grid approximate the Hamilton-Jacobi equation to a prescribed level of approximation.