Applying AXIOM to Partial Di erential Equations
نویسنده
چکیده
We present an AXIOM environment called JET for geometric computations with partial dierential equations within the framework of the jet bundle formalism. This comprises especially the completion of a given dierential equation to an involutive one according to the Cartan-Kuranishi Theorem and the setting up of the determining system for the generators of classical and non-classical Lie symmetries. Details of the implementation are described and examples of applications are given. An appendix contains tables of all exported functions.
منابع مشابه
Numerical Solution of fuzzy differential equations of nth-order by Adams-Bashforth method
So far, many methods have been presented to solve the rst-order di erential equations. But, not many studies have been conducted for numerical solution of high-order fuzzy di erential equations. In this research, First, the equation by reducing time, we transform the rst-order equation. Then we have applied Adams-Bashforth multi-step methods for the initial approximation of one order di erentia...
متن کاملAn introduction to implicit partial di¤erential equations of the rst order
We will discuss here Dirichlet problems for non linear rst order partial di¤erential equations. We will present the recent results of DacorognaMarcellini on this subject; mentioning briey, as a matter of introduction, some results on viscosity solutions.
متن کاملA (rough) Pathwise Approach to Fully Non-linear Stochastic Partial Differential Equations
In a series of papers, starting with [Fully nonlinear stochastic partial di¤erential equations. C. R. Acad. Sci. Paris Sér. I Math. 326 (1998), no. 9] Lions and Souganidis proposed a (pathwise) theory for fully non-linear stochastic partial di¤erential equations. We present here a (partial) extension towards certain spatial dependence in the noise term. The main novelty is the use of rough path...
متن کاملSchur complement preconditioning for elliptic systems of partial differential equations
S hur omplement pre onditioning for ellipti systems of partial di erential equations D. Loghin and A. J. Wathen One su essful approa h in the design of solution methods for saddle-point problems requires the eÆ ient solution of the asso iated S hur omplement problem ([26℄, [19℄). In the ase of problems arising from partial di erential equations the fa torization of the symbol of the operator an...
متن کاملForward – backward stochastic di erential equations with nonsmooth coe cients
Solvability of forward–backward stochastic di erential equations with nonsmooth coe cients is considered using the Four-Step Scheme and some approximation arguments. For the onedimensional case, the existence of an adapted solution is established for the equation which allows the di usion in the forward equation to be degenerate. As a byproduct, we obtain the existence of a viscosity solution t...
متن کامل