analytical solution Definition and Topics - 11 Discussions
In mathematics, a closed-form expression is a mathematical expression expressed using a finite number of standard operations. It may contain constants, variables, certain "well-known" operations (e.g., + − × ÷), and functions (e.g., nth root, exponent, logarithm, trigonometric functions, and inverse hyperbolic functions), but usually no limit, differentiation, or integration. The set of operations and functions admitted in a closed-form expression may vary with author and context.
Hi, I ran into problems using the poisson ratio.
For a FE simulation I created a simple 2D 1mm x 1mm block, and prescribed a 0.1 mm displacement at the top edge.
Furthermore, the bottom edge is constraint in the y-dir, and the left edge in the x-dir.
The material parameters are E = 100, and v...
Hi All,
I'm looking for an analytical solution to the open channel rectangular fluid flow profile. The flow is bounded by three walls but the top is open to atmosphere. Assume steady state flow that is parallel and incompressible.
I've already found information involving a rectangular flow...
I am trying to find a closed-form (analytical) solution for the two following simultaneous integro-differential equations :
du[x]/dx= - a v[x] +b ∫〖[1-(y-x)^4 〗].(v[y]-v[x])dy
And
(dv[x])/dx= - f u[x] -g ∫〖[1-(y-x)^4 〗].u[y]dy
With the initial conditions:
v[0]=e and u[1]=0
a,b,f,g...
Hi all,
I have derived a differential equation, which I don't know how to solve. I can do some numerical simulations, but would really be interested in, at least, knowing if an analytical solution exists, so would appreciate any help with it: (I have removed argument from y)...
I would like to prepare 50.0 g of 50 ppb Pb standard solution in 1% HNO3 gravimetrically, in a 50.0mL plastic tube from a stock solution of 50 ppm Pb.
From what I understand, this is a dilution...so C1V1 = C2V2
I like working in mg/L more than ppb and ppm so I converted
50 ppb = 0.05 mg/L
50...
Hello guys!
I have following differential equation mx"(t)+b(x'(t))x'(t)+k(p)x(t)=0. As can be seen, "attenuation term" is dependent of velocity x'(t).
Also stiffness term k(p) is dependent of term p, which is p=k(p)x(t)/A. In this equation A is constant and k(p) means, of course, same term as...
I have the following system of equations with variables ##a,m##, and I'm wondering—can this system be solved symbolically/analytically?
\begin{align}
m &= 100 + \frac{ \left( 200 \frac{\ln{\frac{1}{2}}}{26.8} \right) }{\left(\dfrac{\ln{\frac{1}{2}}}{26.8} + a \right)}
\\ \\
50 &= me^{-a\left(...
Although this could fall under engineering, I thought the Diff Eq forum was the most relevant. Let me know if I should post elsewhere.
I have a fairly basic system for which I'm trying to find a minimum-time optimal control policy. I know there are many ways to do this numerically, but since...
Hi there
I am trying to find bound state energies assuming infinite potential. I have been told it can be done by analytically solving Right Hand Side and Left Hand Side of an equation such as:
E^1/2 tan(2ma^2E/4hbar)^1/2 = (V0-E)^1/2
If solved properly, it should give one curve (RHS), crossed...