4
votes
0answers
103 views

What differential equation might model this almost-harmonic oscillator?

I need to precisely control the motion of a damped, driven (nearly) harmonic oscillator: $$ \ddot x(t) + \alpha\dot x(t) + \omega_0^2 x(t) \approx V(t) $$ I use the $\approx$ symbol because this is ...
0
votes
1answer
39 views

How can I solve an ODE when $F(x_0)=F'(x_0)=0$ is given at an unknown point $x=x_0$ using bvp5c?

I'm attempting to solve the following ODE using MATLAB bvp5c. I've used bvp5c for other typical multipoint boundary value problems but I have no idea how to deal with ODEs with conditions given at an ...
0
votes
0answers
64 views

Financial mathematic with Feynman-Kac

I have a really big task in financial mathematics and a small part of it (to set up the problem), I need to write a PIDE (the Feynman-kac) where we estimate options with jumps. It is derived from the ...
0
votes
0answers
47 views

Estimate parameters in $y=y_{0}(1-\frac{t}{\tau})e^{-\alpha t/\tau}$

Given the function $y(t)$ with two independent parameters $\tau$ and $\alpha$ $$ y=y_{0}\left(1-\frac{t}{\tau}\right)e^{-\alpha t/\tau}, $$ We have two data points (experimental data) $ ...
3
votes
0answers
131 views

How to solve the advection equation with spiral motion

The advection equation is : $$\frac{\partial f(x,y,t)}{\partial t} + \nabla_{(x,y)} \cdot (A f)= 0$$ With initial condition $f(x,y,0) = f_0(x,y)$. If the vector $A$ is constant, ie. $A = ...
2
votes
1answer
639 views

Python numerical solution for a nonlinear second order ODE with two boundary conditions

I want to solve numerical the next equation, in Python $$u''(x) = \left( a - \Big(b\big(u(x)^{2}\big)\Big) \right) \big(u'(x)\big)^{3}$$ it is a nonlinear second order $ODE$ with two $B.C$. ...
3
votes
1answer
109 views

Iterative model fitting

I have a sequence of points $\{(x_k,y_k,z_k)\}$ and I need to fit some $2D$ model $P(x,y)$ that approximates $z$ in some sense. The $z_k$$'s$ are noisy samples of some $2D$ function $z_k = f(x,y) + ...
0
votes
1answer
116 views

Non-analytical equation

Suppose I have integrated a differential equation numerically using some time-interval $\delta t$. How might I determine the accuracy of the result? Does solving simultaneous equations reduce the ...
3
votes
3answers
97 views

Is there a formal name for a mathematical model that has an overly sensitive parameter

I'm a software engineer with a bit of mathematics expertise working with an NGO that has developed mathematical models for ecosystem services. It turns out that one of these models is overly ...
-1
votes
1answer
622 views

NDSolve simple matrix problem in mathematica

I have a problem with command NDSolve in mathematica. If we have simple second order differential equation, it is easy to write code in mathematica. But if we have matrix problem (for example 4 ...
1
vote
1answer
315 views

What is a 4-8 mesh?

A paper I'm reading uses this classification for a mesh, but I'm not sure what the numbers 4 and 8 signify. Could someone clarify? Here's an image from the paper of a 4-8 mesh.