Questions tagged [differential-equations]

The tag has no usage guidance.

29 questions with no upvoted or accepted answers
Filter by
Sorted by
Tagged with
3
votes
0answers
317 views

MATLAB: solving multiple ODE systems in parallel

I have a system of parameterized ODEs that I would like to solve using MATLAB and its ode45 solver, and was wondering if it is possible to perform such a task in ...
2
votes
0answers
50 views

Numerical errors due to terms of the form $\frac{1}{r}$ (r goes to 0 at the boundary) while using finite difference method

I am trying to solve a system of differential equations using finite difference method. There are few terms of the form $\frac{A(r)}{r}$, both $A(r)$ and r go to zero at the boundary. Analytically ...
2
votes
0answers
60 views

Numerical integration of SDE: choice of $dt$ and algorithm

I am working on the following Stochastic Differential Equation (SDE) in the Quantum Mechanics context: $$dX_{t} = a X_{t} dt + b X_{t} dW$$ where $X_{t}$ is my stochastic varible, $dt$ is my ...
2
votes
0answers
79 views

How to implement adaptive step size Runge-Kutta Cash-Karp?

Trying to implement an adaptive step size Runge-Kutta Cash-Karp but failing with this error: ...
1
vote
0answers
19 views

Optimality conditions for optimal control: BVP - DAE

I am solving an optimal control problem of the form $$ \min_u \qquad\int_0^T \langle u(t), u(t) \rangle \, \mathrm{d}t \\ s.t. \quad \dot{x} = \tilde{f}(x) + u, \quad x(0)=x_0 \\ \qquad \tilde{\Phi}(...
1
vote
0answers
59 views

Are linear, CTCS codes always stable?

I would like to solve some equations which basically look like this $$\frac{\partial u}{\partial x}=F\left(v,\frac{\partial v}{\partial y},\frac{\partial^2 v}{\partial y^2}\right),$$ $$\frac{\partial ...
1
vote
0answers
54 views

Stably solve transport equation with source term

I am trying to solve a transport equation of the form for the variable $\psi(t,r)$ \begin{equation} \partial_t\psi-\alpha(r)\partial_r\psi-\beta(r)^2\psi-f(t,r)=0 , \end{equation} where I am solving ...
1
vote
0answers
28 views

Book Recommendation: Analysis and design of mechanistic models - such as pharmacokinetics or hydrology models

I have been looking at an interesting book "Pharmacokinetic-Pharmacodynamic Modeling and Simulation" by Peter Bonate on pharmacokinetic models: the models of how medical drugs work their way through ...
1
vote
0answers
52 views

Governing equations vs Transport equations

This is a basic question. But I did not find any explanations for this. How are governing equations, like mass, momentum, energy conservations equations, different from 'Transport equation'?. Is a ...
1
vote
0answers
80 views

Solved : Damped spring-mass system, wrong position, correct speed and acceleration

I am modulating a spring-mass system with gravitation and aero drag, with python programming. The spring is hanging vertically and attached a weight. The user then selects a length to drag it down ...
1
vote
0answers
38 views

Why does the correlation function of this stochastic differential equation starts at different points?

I am working with the following differential equation: The equation is $$x=\beta +\sqrt{2D} \xi(t)$$ where $\xi(t)$ is a white noise term, with a reflecting wall boundary conditions. After solving ...
1
vote
0answers
39 views

Numerically solving a system of parabolic PDEs and 1st order ODEs

I'm trying to solve the following system of differential equations numerically. What are the available finite difference approaches and matlab solvers to solve such a system? Other approaches to solve ...
1
vote
0answers
93 views

How to solve an implicit ODE with forward Euler?

Consider the implicit ODE $$ M(y)\dot{y} = F(t,y) $$ If $M$ is non-singular for all $y$ How to use the forward-Euler method to numerically solve for $y$ without inverting $M(y)$? I only came out ...
1
vote
0answers
63 views

fourth order Poisson iterative solver --in Matlab

I want to calculate the stream function $\psi$ starting from a velocity field $(u,v)$ (such that $u=-\frac{\partial\psi}{\partial y}$ and $v=\frac{\partial\psi}{\partial x}$). I thus calculate the ...
1
vote
0answers
16 views

Procedure to identify characteristic properties of unknown functions in a DAE model

I have a system of 1st order odes given by $$ \dot{x_1}(t) = \alpha_1 f_1(x_1,t) + \beta_1 u(t) \\ \dot{x_2}(t) = \alpha_2 f_2(x_2,t) + \beta_2 u(t) $$ They are constrained by an algebraic equation ...
1
vote
0answers
51 views

Second-order PDE with seven variables

I need to solve the following partial differential equation in seven variables with four boundary conditions. I don't think Mathematica has the capacity to solve this differential equation. Do you ...
1
vote
0answers
49 views

Eigenvalue ODE in Spherical Coordinates--Numerical

I wish to solve an eigenvalue problem: $$\nabla^{2}f=Ef $$ If I assume spherical symmetry $f(r,\theta,\phi)=f(r)$, I can reduce the problem to 1D: $$(\frac{2}{r}\frac{d}{dr}+\frac{d^{2}}{dr^{2}})f=...
1
vote
0answers
145 views

Solving complicated coupled ODE using RK4/ODE45 in Matlab

I have the following coupled differential equations also known as Guiding Center Approximation. It is used to explain the position- and velocity change of particles (electrons and protons, N = 1000) ...
1
vote
0answers
91 views

Code for solving the heat equation on the semi-infinite rod

Cross posted in mathematica.SE. Question : I want to test the solution which is given below is right by Matlab/Maple/Mathematica. Please look the post in mathstackexhange or Please look below. ...
1
vote
0answers
159 views

Implementing Neumann boundary condition in nonlinear integro-differential equation

Problem I would like to solve a nonlinear integro-differential equations on a 2D square domain $\Omega$ subject to Neumann boundary conditions using finite differences: $$\frac{\partial u}{\partial t}...
1
vote
0answers
47 views

How is the Gastner-Newman equation implemented to create value-by-area cartograms?

There is a paper called "Density-equalizing map projections: Diffusion-based algorithm and applications" by Michael T. Gastner and M. E. J. Newman, which explains their algorithm (which is based in ...
0
votes
0answers
19 views

Online Parameter Estimation

I have a system $\ y = θ^*u+d(t) $ where $\ y $ is the output , $\ u $ is the input which satisfies $\ u\epsilon L_{\infty} $, $\ θ^* $ is an unknown but constant parameter and $\ d(t) $ is an unknown ...
0
votes
0answers
137 views

Numerically solving a partial differential equation in python with Runge Kutta 4

I'm supposed to solve the following partial differential equation in python using Runge-Kutta 4 method in time. $$ \frac{\partial}{\partial t}v(y,t)=Lv(t,y) $$ where $L$ is the following linear ...
0
votes
0answers
21 views

Offline Parameter Estimation for second order system - Ordinary Least Squares

I have a second order system which is described by the following differential equation: $\ \ddot{y}+α_{1}*\dot{y}=b_{0}*u $ where $\ y $ is the output of the system and $\ u $ is the input of the ...
0
votes
0answers
65 views

How one can simulate a system given by differential equation?

I want to simulate a diffusion environment given by the differential equation $$\frac{\partial u(x,y,t)}{\partial t}=D\left(\frac{\partial^2 u(x,y,t)}{\partial x^2}+\frac{\partial^2 u(x,y,t)}{\...
0
votes
0answers
57 views

What are the differences between these different forms of equation?

What are the differences between Conservative differential form, Non-conservative differential form, Conservative Integral form and Non-conservative integral form of differential equations? I know ...
0
votes
0answers
81 views

why I cannot find explicit finite difference for elliptic equation

Let us think on the Poisson equation $\nabla^2 u(\bf{x})=\rho(x)$ with Neumann boundary conditions, with $\bf{x}=\it (x,y)$ in 2D. Here is a stencil with central differences in both $x$ and $y$ (...
-1
votes
0answers
37 views

What is going wrong in the way I set up constraints for optimization solver?

I have the following dynamical system, Equation 1: $\frac{d \phi}{dt} = -M^TDM\phi$ Equation 2: $\frac{d \hat\phi}{dt} = -M^T\tilde{D}M\hat \phi$ Equation 1 represents the exact dynamics of a ...
-1
votes
0answers
35 views

Solving a 2-time Volterra integro-differential equation

In non-equilibrium field theory one usually encounters the so called Kadanoff-Baym equations, which are Volterra integro-differential of 2 times $$ i \partial_t f(t,t^\prime) = h(t) f(t, t^\prime) + \...