Analytical solution Definition and 64 Threads

  1. P

    Nonlinear ODE: Analytical Solution?

    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)?
  2. F

    Does this series have an analytical solution?

    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
  3. R

    Analytical solution for circular cavity under internal pressure

    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...
  4. A

    Analytical solution of an integral

    Can anyone help me about analytical solution of this Integral? the integral is written in the word file attached here. Many Thanks in advance, Ashkan
  5. P

    Looking for an analytical solution for a quadratic attractive potential well

    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...
  6. G

    Solving PDE with Analytical Solution: Exploring LaTex Code and Techniques

    LaTex Code: \frac{\partial U}{\partial t} + ax\frac{\partial U}{\partial x} + b\frac{\partial^2 U}{\partial x^2} = 0 Can someone please tell me how to solve this PDE? Thanks, Geoff
  7. A

    MATLAB Problems in finding analytical solution in Matlab

    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...
  8. R

    Analytical Solution to Poisson's Equation

    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.
  9. F

    Analytical Solution to this? - linear system of ODES

    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...
  10. N

    Analytical solution of Laplace's equation with horrendous boundary conditions

    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...
  11. M

    Solving Nonlinear ODEs with Trigonometric Functions in Physics

    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...
  12. U

    Can an analytical solution for PRKE be found with ramp reactivity ?

    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...
  13. C

    Analytical solution for coupled ODE's

    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...
  14. R

    Solving (1/α) * dT/dt for Exact Analytical Solution

    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...
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