Questions on the symbolic (DSolve, DifferentialRoot) and numerical (NDSolve) solutions of differential equations in Mathematica.

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9
votes
1answer
2k views

Bifurcation diagrams for multiple equation systems

I am interested in constructing a bifurcation diagram for some of my parameters (especially for β and γ) in the dynamical system given in the code below. I want to see how parameter changes affect the ...
1
vote
1answer
864 views

Mathematica won't solve equation I know is solvable

I'm just trying to solve the Schrodinger equation for hydrogen. We went through the solution by hand in class but Mathematica doesn't do anything when I try to solve it (it just re-displays what I ...
2
votes
1answer
647 views

Differential equations with jump conditions

Suppose I want to solve an ODE with a DiracDelta source term. In the following example, DSolve does it correctly while ...
7
votes
3answers
868 views

How to manipulate gauge theory in Mathematica?

I want to know if there is a way of typing into Mathematica an expression like the following, $$\epsilon^{\mu \nu \lambda} f^{abc} A^a_\mu A^b_\nu A^c_\lambda + g\epsilon^{\mu \nu \lambda} A^a_\mu ...
1
vote
1answer
194 views

Find the derivatives of arbitrary order of a function found using NDSolve

For the following initial value problem BC[b_]:=x[0]==b; eq[b_]:=NDSolve[{equation==0, BC[b]}, x, {t,0,1000}]; body[t_,b_]:= x[t]/.eq[b]; one could define the ...
0
votes
2answers
239 views

System of ODEs specified by large coefficient matrices

What is the best way to call NDSolve for solving a system of differential equations of the form ...
0
votes
1answer
157 views

Extract a value from a list of InterpolatingFunction

By running the code n = 5; U[t_] := Table[Subscript[u, i][t], {i, 0, n}]; lines = NDSolve[{eqns, initc}, U[t], {t, 0, T}] I get the output ...
3
votes
1answer
326 views

Partial differential equation: unexpected result from changing boundary region size

I am trying to solve a PDE for heat diffusion, but I have a problem with the boundary region. When I change the boundary region size, the estimation of temperature increases even when no other ...
1
vote
0answers
367 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 ...
2
votes
0answers
675 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: ...
1
vote
1answer
2k views

problem solving coupled second order differential equations using Dsolve

I have three coupled second order ODE's given as below $x''[t] = -c_1*y'[t]-c_2*z[t]-c_3$ $y''[t] = -c_4*x'[t]$ $z''[t] = \frac{c_5}{c_6}*x[t]-c_6$ where $c_i$'s are know constants. The ...
2
votes
2answers
425 views

Plotting several numerical solutions plus the analytic solution of ODE in one plot

I want to be able to plot several numerical solutions of an ODE plus its analytical solution in one plot in order to see how the numerical solutions converge towards the analytical one w.r.t. the ...
7
votes
2answers
2k views

NDSolve with vectors

I'm stumped. I'm trying to write this using vectors, but the 2nd derivative isn't being expanded like I expected it to be. This is a system of equations for a projectile with quadratic drag and ...
5
votes
1answer
981 views

Solve system of ordinary differential equations that doesn't have an initial condition (t=0), but has an inifinity condition (t=infinity)?

I have a question for solving t -> Infinity on Mathematica. First, I have a system of ODEs: ...
2
votes
1answer
246 views

How to solve a system of ordinary differential equations contain a interpolating function?

I'm wondering how I can solve a system of ODE that has a interpolating function? For example, z and y are ...
12
votes
1answer
2k views

Numerically solving an inhomogeneous partial differential equation

I'm trying to solve a cylindrical partial differential equation with boundary conditions. But I got an error message saying ...
16
votes
3answers
16k views

Plotting a Phase Portrait

I'm trying to plot a phase portrait for the differential equation $$x'' - (1 - x^2) x' + x = 0.5 \cos(1.1 t)\,.$$ The primes are derivatives with respect to $t$. I've reduced this second order ODE to ...
5
votes
2answers
7k views

How do I solve coupled ordinary differential equations?

I have four coupled ODE's. I am not sure how to plot and solve them using Mathematica. I won't give the exact problem, but the following is something analogous: The equations ...
5
votes
1answer
1k views

How do I find the best parameter to fit my data if the model is a interpolating function?

Hi I have a question regarding to find the best parameters for my model to fit my data. I have 3 ordinary equation, and I now just picked some parameters (...
2
votes
2answers
2k views

How to decouple a first order ODE system by eliminating coupled functions

Let's see an example of a first order ODE system : $$\begin{align*} y_1'&=a_{11}\cdot y_1+a_{12}\cdot y_2 \qquad(1)\\ y_2'&=a_{21}\cdot y_1+a_{22}\cdot y_2 \qquad(2) ...
1
vote
4answers
2k views

How do I plot x[t] vs. x'[t] (where x[t] and x'[t] are solutions to NDSolve)?

I have a differential equation which I solved using NDSolve. I can easily plot x[t] vs. t, x'[t] vs. t, but.... how do I plot x[t] vs. x'[t]? I tried using the Evaluate function to simplify things, ...
1
vote
0answers
334 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
1answer
500 views

How to plot population growth model?

How would I draw the graph of a function dy/dt=((Ry^2)/T)-Ry in Mathematica? I have tried a few times but the constants are confusing me.
9
votes
1answer
255 views

The only usage for the option InterpolationOrder in NDSolve is to be set to All?

We know that changing the option InterpolationOrder in ListLinePlotListPlot3D、...
2
votes
2answers
773 views

Problem with NDsolve for a system of equations

I want to solve a system of differential equations which is not very complicated, but I cannot handle the problem with mathematica!! Please have a look at the problem and result and help me with your ...
3
votes
0answers
422 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 ...
5
votes
3answers
619 views

Numerical solution of a differential equation with NIntegrate coefficients

I am trying to solve a linear ODE with a variable coefficient which is given in terms of an integral I can only do numerically. That is, I have an equation of the form $$ ...
3
votes
1answer
459 views

Solving the Sine Gordon PDE in mathematica

how can i solve this equation in mathematica? this is sine-gordon eq. but the boundary condition can not recognized by mathematica . thank you for you attention. ...
3
votes
1answer
199 views

Construct DifferentialMatrices and Kernel for LevinRule for this integral and ODE set

I've made a lot of progress on my problem the last few days thanks to all the help I've received on here. I think I'm upto the final step of greatly improving the performance of NIntegrate[..] on my ...
2
votes
2answers
926 views

No result from DSolve

I don't get any answer when I evaluate the following expression: ...
2
votes
1answer
401 views

Vector Analysis: Why are the Grad, Laplacian and Div being evaluated to zero

For the non linear partial differential equation below, why are the Gradient, Laplacian and Divergence being evaluated to zero despite using the VectorAnalysis ...
4
votes
1answer
2k views

Finding the Minimum value of an interpolating function

I can't seem to use FindMinValue to find the min. value of a curve represented by an interpolating function. For instance the below code generates an interpolating ...
14
votes
3answers
596 views

How to perturb a Dynamic System?

I'm trying to model a basic feedback system with delayed feedback. I've done the initial setup and now want to add a few more advanced features to my system. Currently, it's just a simple ...
1
vote
1answer
302 views

Why is NDSolve solving in term of two 1st order ODE slower than 2nd order?

As mentioned in the documentation for NDSolve it's often convenient to reduce a 2nd order ODE to a system of first order equations. When I do this however I seem to see a significant speed reduction ...
2
votes
1answer
779 views

NDSolve runs out of memory

I need to solve a second order ODE numerically. The ODE depends on two parameters (a,b). Things work fine when 'a' is small, but for large 'a' the solutions are oscillating rapidly and Mathematica ...
11
votes
3answers
4k views

NDSolve with Euler method

I want to solve this equation with NDSolve[] using the Euler method: x'[t] == 0.5*x[t]-0.04*(x[t])^2 with initial condition ...
14
votes
1answer
1k views

Poisson solver using Mathematica

I am looking for some help with a Poisson solver I am writing in Mathematica. The code is quite long with Arrays plugged in, so the full details can be found at http://pastebin.com/uSrSDcW6 I am ...
8
votes
1answer
768 views

1D Euler Equations

Is it possible to accurately solve the 1D Euler equations in Mathematica using NDSolve? For example, let us consider the problem given here: http://www.csun.edu/~jb715473/examples/euler1d.htm Using ...
5
votes
1answer
583 views

Unexpected results from NDSolve

I am trying to solve a stiff reaction diffusion system with NDSolve. However, it does not produce the expected results. My problem is a spherical cell with 5 ...
3
votes
1answer
1k views

Improving NDSolve speed for heavily stiff problems

Having looked around the intergoogles and Mathematica.SE, I thought I'd pose a question with a minimum working example. Here is the situation I am trying to improve: I am solving a 4th order non ...
8
votes
2answers
5k views

Integral equation numerical solution with NDSolve

I'm trying to solve something like: f[x] == Integrate[f[x]*g[x]] where g[x] is known and ...
3
votes
1answer
467 views

Second Order Non Linear Differential Equation

I'm trying to solve the following differential equation numerically: ...
5
votes
0answers
245 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 ...
2
votes
1answer
198 views

tricky memoization

Let's say I have the NDSolve example for documentation involving splitting 2nd order into set of 1st order ODEs: ...
3
votes
1answer
423 views

Efficient way to perform elementary integration step with NDSolve internal method

I'm trying to tweak the NDSolve function to perform one elementary integration step (using some explicitly selected stepping algorithm via ...
2
votes
1answer
772 views

Solving a PDE containing DiracDelta

I want to get the answer from a PDE: $$\begin{align*} \frac{\partial \rho(r,t)}{\partial t}&=Dr^{-2}\frac{\partial}{\partial r}r^2h(r)e^{-U(r)}\frac{\partial}{\partial ...
0
votes
1answer
514 views

Solving Differential Equation depending on variables solved by NDSolve

How to solve a differential equation which consists of variables depending upon another differential equation?
2
votes
1answer
139 views

Using MaxStepFraction as ticks on plot

Is there any way I could use the MaxStepFraction (or grid size) as used in NDSolve in the example below as ticks on the 3d Plot? ...
1
vote
2answers
443 views

Replacing variable in an equation with an Interpolating function polynomial and plotting residual

I was trying to plot the residual for the solution of my PDE. However, I was unsure about a couple of things. I imported the data and created an Interpolation polynomial with ...
2
votes
0answers
189 views

EventLocator with LSODA?

Is the EventLocator option not compatible with LSODA on NDSolve. Below is what I tried to do ...