Questions on the symbolic (DSolve, DifferentialRoot) and numerical (NDSolve) solutions of differential equations in Mathematica.
3
votes
1answer
180 views
Is it possible to impose “Assumptions” in DSolve or equivalent? (differential equation solving)
When DSolve tries to solve differential equations, it is sometimes not smart enough to generate conditions according to different possible value of parameters. ...
7
votes
0answers
162 views
Numerically solve 2nd order differential equation with singularity
Consider a second order differential equation with a potential that diverges at some generic value in the variable. For example:
$$-y^{\prime\prime}(s)+\frac1{\mathrm{cn}{(s\mid k^2)}}y(s)=0$$
where ...
7
votes
0answers
1k views
Integro-differential equation
I have to numerically solve a nonlinear partial integro-differential equation using Mathematica. This is my equation,
$$\frac{\partial y(x,t)}{\partial t}=\int_{-\infty}^\infty K_0(|x-u|) ...
6
votes
0answers
64 views
Modify NDSolve`StateData (if possible)
I am trying to solve a PDE that needs to be scaled constantly (refer to this). @andre suggests I modify NDSolve`StateData.
Now, the problem is, I'm not used to ...
6
votes
0answers
232 views
Modeling neural excitation with a non-linear differential equation
I think I have a special problem and I am not sure how to search for an answer, so I thought I would try here.
I am working with the so called FitzHugh-Nagumo model which describes very simple ...
6
votes
0answers
70 views
Return partial result when MemoryConstrained aborts NDSolve
I use NDSolve to solve a large set (~400) of coupled ODEs. Sometimes, the memory (~4GB) gets filled up, and my computer becomes impossible to work with, because it ...
5
votes
0answers
168 views
Second-Order Feedback Pathways
I'm relatively new to Mathematica and I've tried searching and reading through the Mathematica documentation but I'm not able to find a good place to start.
I want to model a simple, second-order ...
4
votes
0answers
419 views
Controlling the time step in NDSolve?
I generally use NDSolve for stiff non linear partial differential equations of 4th order. I find that a BDF1 method generally does well to placate my beast of a PDE.
I've also tried out ...
3
votes
0answers
82 views
Using NDSolve for Integro-Differential Equations
I have a fairly complicated set of coupled non-linear integro-differential equations that I am trying to solve using NDSolve. The equations are:
...
3
votes
0answers
70 views
Symbolic solution to ODE, pure InverseFunction not evaluated
I'm new to Mathematica and I don't understand why in the solution of the following ODE, the #1 in the pure function is not immediately replaced by the corresponding ...
3
votes
0answers
239 views
Numerically solving PDE with high precision
I want to numerically solve the PDE
$\partial_t u(t,x)=c\partial_x u(t,x)+(mx-l)u(t,x)$
with some initial and boundary conditions and given parameters $c$, $m$ and $l$.
Consider the code
...
3
votes
0answers
426 views
How to Solve this ODE with Mixed Boundary condition
I have an ODE equation which is sort of
y''[x] + 2 y'[x]/x + .0001 (y[x])^3 ==0
subject to the boundary conditions
...
2
votes
0answers
82 views
Conditional statements in intial conditions?
This is potentially a daft question, but I thought I'd ask it; I have some material free to diffuse in a boundary between rn and ro; I've been able to get it working nicely for neumann type boundary ...
2
votes
0answers
130 views
Kalman filter by hand
I am now learning the Kalman filter and wants to implement it by hand to understand it better. To be specific I want to first simulate a sequence of data by
$$
\dot x=Ax+Bw\\
y=Cx+Dv,\\
...
2
votes
0answers
94 views
differential equations with implicit functions
I have an ordinary differential equation that contains coefficient functions that depend implicitly on the independent variable via an algebraic equation. I am trying to go ahead and use NSolve to ...
2
votes
0answers
216 views
Inconsistent boundary and initial conditions: BC ignored altogether
Consider the following diffusion-decay equation with von Neumann b/c in the origin and Dirichlet at the other boundary:
...
2
votes
0answers
128 views
EventLocator with LSODA?
Is the EventLocator option not compatible with LSODA on NDSolve. Below is what I tried to do ...
1
vote
0answers
97 views
Solving first order ODE by Runge-Kutta method
I want to solve the first order ODE by the Runge-Kutta method of order 4 $$y'(x)=1+(E-V(x)-1)\sin^2(y(x)),\qquad{}V(x):=\begin{cases}
-20\left(1+36x^2\right)(x+1)^2(x-1)^2&\hbox{if }|x|<1,\\
...
1
vote
0answers
140 views
Can my ODE be solved? And, if so, how?
The equation is
-y''[x] + u*y[x] - y[x] == 0
where
u = -Sum[1/Abs[x - n], {n, -Infinity, Infinity}]
with periodic ...
1
vote
0answers
73 views
What is wrong with this PDE?
I'm trying to get a numerical solution to the wave equation but Mathematica keeps on giving me an error and I cannot see what the problem is. This is the code I have:
...
1
vote
0answers
103 views
Performance in parameter estimation from ParametricNDSolve using varied initial conditions
I have 250 data points from a timecourse exeriment in a list, with columns specifying (1) time, (2-4) initial conditions, (5) absorbance reading. I want to fit 4 parameters (k1, k2, k3, k4) in a DAE ...
1
vote
0answers
131 views
Adapting NDSolve to circumvent NDSolve::bdord: error for 1-D Euler Equations
I attempted to use NDSolve for the 1-D isentropic unsteady flow equations with low subsonic inflow velocity and prescribed inflow total enthalpy; along with a ...
1
vote
0answers
125 views
NDSolve equations contain solution from solving cubic equations
I'm having trouble using NDSolve to solve equations that were obtained from solving cubic equations.
In my problem, I first obtained 6 functions (ca1, ...
1
vote
0answers
155 views
NDSolve error when solving a BVP
I'm trying to solve the following BVP with unknown parameters (p and phi) using NDSolve over the period {Pi, 2 Pi}:
...
1
vote
0answers
213 views
Coulomb/kepler potential dynamics. NDSolve breaks
I've been trying to do a simple dynamics in coulomb potential (electron(s) around a nucleus). My equations break down. I think it's because of 1/0.
is there a way ...
1
vote
0answers
121 views
NDSolve Convergence test failure and significant effect of DifferenceOrder on eventual results
I am solving a non linear partial differential equation with what I call free boundary conditions (solid mechanicists would know this as simply supported).
I realized that this boundary condition ...
1
vote
0answers
139 views
Issue concerning stopping NDSolve through EventLocator
Greetings. As the question-title is written I am having some trouble with getting a numerical integration stopped at a certain event. This integration is done through the use of NDSolve and I have ...
1
vote
0answers
201 views
1
vote
0answers
340 views
Effectively Dirac delta in numeric PDE - Mathematica or Matlab solution?
I am trying to solve a following Partial Differential Equation:
u_t(x,y,t)= u_xx(x,y,t)+u_yy(x,y,t) + 7 u(x,x,t)
which causes troubles due to the last term ...
0
votes
0answers
63 views
Non-Solvable PDE?
I would like to know whether this PDE is solvable and if yes, for which values of $a$.
...
0
votes
0answers
56 views
Integrating and plotting pde system solution
I have a trouble with plotting a pde system solution. I'm solving a PDE system in 2-dimensional space and then I want to integrate the solution along one dimension and build a log plot along the ...
0
votes
0answers
46 views
Find leading-order asymptotic approximatons to the solution of epsilon y''+Cosh[x]y'- y == 0
I am trying to solve this boundary value problem and obtain the leading-order approximations using asymptotic matching. But I got my solution wrong and I am stuck along the way, struggling to find any ...
0
votes
0answers
40 views
How to let Mathematica computes the limit if it encounters an indefinite expression when solving ODEs?
The code talks itself clearly:
...
0
votes
0answers
35 views
How can I solve this differential equation for some restricted domain and plot the solution for some values of the parameter
I have encountered some problems when solving this DE. I am wondering if anyone could help me point out the mistakes.
The question says:
Obtain and verify a symbolic solution for ...
0
votes
0answers
52 views
Using NDSolve over a list of functions
I apologize for how messy this explanation will be.
I would like to take a differential equation and iterate that solution over a range of coefficient values. The second part of this is that the ...
0
votes
0answers
59 views
NDSolve: methods and step size choosing
I am looking into the documentation of NDSolve[]; more precisely how this function chooses the StepSize and how it chooses which ...
0
votes
0answers
53 views
DSolve::overdet for system of linear PDEs
I would like to resolve symbolically the following equation:
...
0
votes
0answers
89 views
NDSolve divergence in Mathematica 9
I have been working with Mathematica 7 and 8 to numerically solve partial differential equations by MethodOfLines of NDSolve. ...
0
votes
0answers
58 views
NDSolve::ndfdmc: Computed derivatives do not have dimensionality consistent with the initial conditions. >>
I am trying to solve this NDSolve problem and I am getting the above error and do not know why. Here is what I have:
...
0
votes
0answers
88 views
Need conditions for DSolve
If I have differential equation of fourth order with four solutions $\alpha _1,\alpha _2,-\alpha _1,-\alpha _2 $ where we have appearing the solutions in the form $e^{\text{$i\alpha $}_1 ...
0
votes
0answers
62 views
Inverse problem of Eigenvalues in DSolve
For my graduation exam I must prepare system of equations to satisfy some specific conditions. I have solutions, output 2, but I need equations eq11 and eq22. So here is an example.
...
0
votes
0answers
164 views
Boundary Value Problem
I have to solve this boundary value problem:
$$\frac{\mathrm{d}e_{3x}}{\mathrm{d}l}=(M_0+F_{0z}x-F_{0x}z)e_{3z}$$
$$\frac{\mathrm{d}e_{3z}}{\mathrm{d}l}=-(M_0+F_{0z}x-F_{0x}z)e_{3x}$$
...
0
votes
0answers
201 views
ParametricNDSolveValue or NDSolve + fitting
I have been trying to find the value for the parameter kestim that yields the best fit of a model to some data points. datac has ...
0
votes
0answers
72 views
A good choice to find solutions of ODE
In order to rephrase the question.
I would ask you to take a look at the following problem:
I have this system of ODE:
$$
\begin{cases}
\dot{x}(t)= x(t)[r_1(t) -b_1(t)x(t- \tau(t)) - c_1(t)y^m(t)] ...
0
votes
0answers
120 views
Diffusion equation with concentration dependent diffusivity, NDSolve has problem at C0> 10^20
I am using NDSolve to solve the diffusion equation:
D[Cp[x, t], t] == D[Dc D[Cp[x, t], x], x]
where Dc is a function of ...
0
votes
0answers
136 views
Numerical solution of a system of ODEs
I have to solve set of coupled first order ODE's
$y_1=z$, $ y_2=\frac{dz}{dt} $;
$\frac{d^2y_1}{dt^2}=\frac{dy_2}{dt}=\frac{(p_s-p_f)}{p_s}g-\frac{9u}{2a^2p_s}y_2 $
Using the Euler method and the ...
0
votes
0answers
73 views
Applying individual values (e.g. from a list) to the gain variable of a common PID
I am currently implementing more things into my model of a common kitchen / manufacturing scale and came up with the idea to assign different values to the gain variables of the PID controlling the ...
0
votes
0answers
265 views
Find parameters to fit data with a function
I have a question regarding to find parameters (k1 & k2) to fit functions. At the beginning, I guessed ...
0
votes
0answers
254 views
Unexpected result from contour plot - where is the color gradient?
When I plot a contour plot of my (in)famous code :P I get some unexpected results that I don't quite understand.
My code (the one that has ...
-2
votes
0answers
43 views
Numerical ODE with boundry condition at infinity and singularities
Can Mathematica understand boundry conditions at infinity? What about singularities in numerical ODEs?
