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The program PEEI 4.0.0.1 calculates a numerical solution of every solvable system of partial differential equations. This version 4.0.0.1 has the following improvements over the previous ones. Have been improved the GUI, the management of the execution and the execution itself. Was made available the choice between two different methods of resolution of the total system of equations, labeled 'normal method' and 'other method'. The 'normal method' is essentially the same of the previous versions, but have been improved its performance and its termination criterion. The 'other method' is based on the 'interval analysis' and, although is generally slower, has the advantage of being able to calculate always the best solution. Has a better activation procedure. This program must be reactivated once a month, but is completely free for unlimited personal and business use, and also the reactivation takes place for free and quickly with a button that automatically appears.