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# Tag: solution

## Online traffic policy problem solution

## java – Pattern / solution for Boolean decision making chains

## A complete solution to start a crypto business – HYIPs

## Solution to $ax_1 frac{partial F}{partial x_1} + bar{a} x_2 frac{partial F}{partial x_2} = F$

## Zmatic online traffic solution!

## differential equations – NDsolve Initial Condition is a Function of the Solution

## linear algebra – A matrix Riccati differential equation with constant coefficients? Is there a solution for this in closed form?

## usability – How can I phrase questions to user tests to not give away the solution?

## Zmatic online traffic solution

## Numerical solution for an integro-differential equation

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I need a solution for decision making chain. There are number of criteria that may return true, false or be inconclusive. A non-functional code (Java) would look like this:

```
Boolean res = nullValuesCheck(fieldValue, node);
if (res != null) {
return res;
}
res = typeCheck(node);
if (res != null) {
return res;
}
res = dictCheck(dict, fieldValue);
if (res != null) {
return res;
}
return finalCheck(fieldName, fieldValue); //also returns a Boolean
```

I’m considering creating an extended predicate that would return a nullable `Boolean`

instead of `boolean`

, so that an inconclusive result could be returned.

I tried googling, but found no apparent solution (got lot of mishits on some simple java problems instead). I am wondering whether there exists a pattern, a library maybe, that would handle this problem properly. The problem seems generic and simple to solve and someone must’ve solved it already. I don’t want to reinvent the wheel.

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I’m encountering a PDE taking form of $$ax_1 frac{partial F}{partial x_1} + bar{a} x_2 frac{partial F}{partial x_2} = F,$$ where $ain mathbb{C}$ and $F: mathbb{R}^2 to mathbb{C}$. Can anyone give me a hint on how to solve $F(x_1, x_2)$?

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So this may be a terribly no good bad thing to ask of NDSolve, but it is physically relevant. I am trying to solve something like Fick’s Law:

$$frac{partial varphi}{partial t}=frac{partial^2 varphi}{partial r^2}+F(r,t)$$

Subject to a boundary condition which looks something like:

$$varphi (R,t)=varphi_0-int_0^R varphi(r,t)dr$$

Which is an attempt to simulate the case where whatever is diffusing into the medium of interest is limited in quantity. I assume simply plugging a recursive boundary condition is going to go poorly, is there any option here other than writing my own solver?

The following is a matrix Riccati differential equation with constant coefficient matrices.

$$Dfrac{partial{C(t)}}{partial{t}}S + frac{1}{n}C(t)QDC(t)S – EC(t)Q = 0$$ or

$$Ddot{C}(t)S + frac{1}{n}C(t)QDC(t)S – EC(t)Q = 0$$

given initial condition $C(0) = C_0$.

I stumbled upon this from some other problem and I don’t have any background in matrix differential equations and I’d like to know if there is any way to solve this equation. I read it can be reduced to an algebraic Riccati equation. Is there any closed form expression for solution of this equation? Or anything that is closest to solving this equation?

**Matrix dimensions**

$C(t)$———-> $(m+1)times n$

$S$————–>$ntimes 1$

$Q$————–>$ntimes(m+1)$

$D$————–>$(m+1)times(m+1)$ diagonal matrix. (it is also singular, as there is a diagonal entry that is 0).

$E$————–>$1times (m+1)$

If its useful to know, $n>>m$ and $mge 3$

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– Taboola

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Zmatic

.

I would like to solve numerically the following integro-differential equation

$$ partial_t rho(t,x) ,=, partial_xbig(f'(x),rho(t,x)) int_0^infty f(xi),rho(t,xi),dxi ;+\ +; partial_xbig(g'(x),rho(t,x)) int_0^infty g(xi),rho(t,xi),dxi $$

where:

- $rho$ is a probability distribution on $(0,infty)$ which actually can degenerate to a convex combination of a Dirac delta and a density function;
- the initial condition $rho(0,x)$ can be suitably chosen, such that $int_0^inftyrho(0,x)=1$;
- let’s say the functions $f,g$ are given.

I’ve tried with DSolve, but an exact solution is not found. Then I’ve tried with NDSolve and I get the following error:

**NDSolve::delpde: Delay partial differential equations are not currently supported by NDSolve.**

Is it possible to solve this equation using Mathematica? I am using Mathematica 11.

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