This paper proposes a method of discovering some kinds of di erential equations with interval coe cients, which characterize or explain numerical data obtained by scienti c observations and experiments. Such numerical data inevitably involve some ranges of errors, and hence they are represented by closed intervals in this paper. Based on these intervals, we design some interval inclusions which...

A careful analysis of di erential renormalization shows that a distinguished choice of renormalization constants allows for a mathematically more fundamental interpretation of the scheme. With this set of a priori xed integration constants di erential renormalization is most closely related to the theory of generalized functions. The special properties of this scheme are illustrated by applicat...

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...

An action system framework is a predicate transformer based method for modelling and analysing distributed and reactive systems. The actions are statements in Dijkstra's guarded command language, and their semantics is given by predicate transformers. We extend conventional action systems with a di erential action consisting of a di erential equation and an evolution guard. The semantics is giv...

in this paper, the convergence of zakharov-kuznetsov (zk) equation by homo- topy analysis method (ham) is investigated. a theorem is proved to guarantee the conver- gence of ham and to nd the series solution of this equation via a reliable algorithm.

Multigrid methods are studied for the solution of linear systems resulting from the 9-point discretization of a general linear second-order elliptic partial di erential equation in two dimensions. The rate of convergence of standard multigrid methods often deteriorates when the coe cients in the di erential equation are discontinuous, or when dominating rst-order terms are present. These di cul...

We present a constructive method to devise boundary conditions for solutions of second-order elliptic equations so that these solutions satisfy speci c qualitative properties such as: (i) the norm of the gradient of one solution is bounded from below by a positive constant in the vicinity of a nite number of prescribed points; and (ii) the determinant of gradients of n solutions is bounded from...

In this survey we recall the results obtained in [16] where we gave a representation theorem for the solutions of stochastic di¤erential equations in Hilbert spaces. Using this representation theorem and the deterministic characterizations of exponential stability and uniform observability obtained in [16], [17], we will prove a result of Datko type concerning the exponential dichotomy of stoch...

The ultimate goal of this research is to construct a hybrid model for sound propagation in layered underwater environments with curved boundaries by employing a di↵erential formulation for inhomogeneous layers and a boundary integral formulation for homogeneous layers. The discretization of the new hybrid model is a combination of a finite di↵erence method for the Helmholtz equation for inhomog...