Given a differential equation with infinite-dimensional symmetry pseudo-group it is shown, using an example, that it is generally not possible to construct enough joint invariants to form an invariant numerical scheme of the equation. To circumvent this problem, we propose to discretize the symmetry pseudo-group action. Using the theory of moving frames, joint invariants of the discretized action are algorithmically constructed. Computer simulations indicate that numerical schemes constructed from these joint invariants can produce better numerical results than standard schemes.
On Discrete-Time Approximations to Infinite Horizon Differential Games
Instituto de Investigación en Matemáticas (IMUVA), Universidad de Valladolid（瓦拉多利德大学数学研究所）；Departamento de Matemáticas, Universidad Autónoma de Madrid（马德里自治大学数学系）
Conformally invariant elliptic Liouville equation and its symmetry preserving discretization
Universitá di Roma Tre（罗马第三大学）；INFN, Sezione di Roma Tre（意大利国家核物理研究所罗马三分所）；Universitá del Salento（萨莱诺大学）；INFN, Sezione di Lecce（意大利国家核物理研究所莱切分所）；Université de Montréal（蒙特利尔大学）
