What is Analytical solution: Definition and 64 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.
Nonlinear 1st order ODE
\frac{dH}{dt}=B-A*(H-Z)^{3/2}
where:
B,A and Z are known values
H=f(t); H is function of t
I've already solve this ODE numerically using a 4th order RK routine. But my question is, it is possible to get an analytical solution for H(t)?
Hi all,
Can anyone show how I'd work out the analytical solution to an infinite series of this form:
\sum\limits_{n = 0}^\infty {\exp \left( { - An} \right)}
Thanks in advance,
F
A book listed the problem infinite circular cavity under internal pressure and said there is a analytical solution for stress and displacements but it didn't give any reference.
I have searched many papers and online materials but still couldn't find anything.
The closest thing I found...
I am trying to derive an equation of motion for a simple electrostatic potential well.
Imagine a scenario where an electron (or other charged particle) is released from an arbitrary distance from a fixed (unperturbable) attractive charge (say a proton fixed in space).
In 1 dimension, the...
Hello everybody,
I am a newbie in using Matlab and i have faced a problem i haven't been able to overcome so far,so i decided to share it with you.
I would like to solve the following equation in Matlab:
(-2*t...
I have the equation del^2 phi =1 for 2-d (x and y) with the boundary condition being 0 along all 4 edges. I've looked in all my math books and can't find how to solve this. If anyone could get me started I would appreciate it.
Analytical Solution to this? -- linear system of ODES
Hi All,
It's been awhile since I've even attempted to solve something analytically, so before jumping back into the text. Does the following already have a common solution that I can find somewhere?
Thanks,
dx1/dt = A1 + B1x1...
Hi,
I'm trying to find an analytical solution of Laplace's equation:
\phi_{xx} + \phi_{tt} = 0
with the tricky boundary conditions:
1. \phi(x=0,|t|>\tau)= 0
2. \phi(x\neq0, |t|>>\tau)=0
3. \phi_{x}(x=0, |t|<\tau)=-1
4. \phi_{t}(x, |t|>>\tau)=0
I have the following ansatz(I...
I have a couple ODEs that I need to solve. I was probably just going to put them into mathematica, but I like finding the analytical way also. The first one is
\frac{d}{dx}\left( \frac{(y + \lambda)y'}{\sqrt{1+y'^2}} \right) = \sqrt{1+y'^2}
Lambda is a constant and y' is dy/dx. I...
Hi there,
Before i state what my actual question is, let me give some background on some work i have done on this. I have been trying to solve the 0-D PRKE transient problem for a step and a ramp input numerically using couple of high precision methods.
1) Using MATLAB's inbuilt ode23s...
Hello all,
I wanted to know if there are ways to find analytical solutions for a set of equations defined as follows:
1) x''(z) + B(y,z)*y'(z) + C(y,z) = 0
2) y''(z) + B(y,z)*x'(z) = 0
where ' represents derivative wrt z. and we need to determine y(z) and x(z). B(y,z) and C(y,z) are...
im looking for an exact analytical solution for the following
(1/alpha) * dT/dt = d2T/dr2 + (1/r)*dT/dr
where d is actually dou(partial diff.)
subject to the boundary conditions,
a<=r<=infinity
t>=0
T=Ts (constant) at t=0;
-dT/dr + HT = H(Tf) at r=a; where H, Tf are...