is called a solution of the differential equation. The process of deducing a solution from the equation by the applications ofalgebraandcalculusis called solving orintegratingthe equation. It should be noted, however, that the differential equations that can be explicitly solved form but a small mi...
In this paper we investigate the nature of the adapted solutions to a class of forward-backward stochastic differential equations (SDEs for short) in which the forward equation is non-degenerate. We prove that in this case the adapted solution can always be sought in an "ordinary" sense over...
Using this scheme, we further prove that the backward components of the adapted solution are determined explicitly by the forward components via the solution of a certain quasilinear parabolic PDE system. Moreover the uniqueness of the adapted solutions (over an arbitrary time duration), as well ...
is a solution to our differential equation. You may be deeply skeptical of how we got here, and good for you if you are, but it’s easy to show that this is in fact a solution to our differential equation. Is this worth it? There are other ways to find a solution to our different...
What Is Needed for a Finite Element Analysis To solve partial differential equations with the finite element method, three components are needed: a discrete representation of a region, i.e. a mesh a partial differential equation boundary conditions that link the equation with the region This ...
Its basic idea is that outflow from a cell is treated explicitly while inflow is treated implicitly. Since the matrix of the system in this new I2OE method is determined by the inflow fluxes it is an M-matrix yielding favourable solvability and stability properties. The method allows large ...
(2) unfixed excitation mode. Among them, the fixed excitation mode adaptively recalibrates the per-channel feature responses by explicitly modeling interdependencies between the channels using a shared excitation block for each hidden layer. The unfixed excitation mode employs different excitation blocks ...
As for the boundary condition, because g is explicitly given, we require that 𝑢̂u^ interpolates u at some boundary points. In spirit, the function 𝑢̂u^ is a kind of interpolator of u, like 𝑠(𝑥)s(x) in Equation (2). The coefficients 𝑐𝑖ci in Equation (2) can ...
collinearity and concyclicity. This graph data structure bakes into itself some deduction rules explicitly stated in the geometric rule list used in DD. These deduction rules from the original list are therefore not used anywhere in exploration but implicitly used and explicitly spelled out on-demand...
A trial solution of the differential equation is written as a sum of two parts. The first part satisfies the boundary (or initial) conditions and contains no adjustable parameters. The second part is constructed so as not to affect the boundary conditions. This part involves a feedforward ...