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

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0
votes
1answer
212 views

Solving a simple BVP

I'm new to mathematica and am interested in solving the following BVP: $\epsilon \,y'' + 2 y' + y^3 = 0$, for $0 < x < 1$ and $y(0) = 0, y(1) = 1/2$. I have no experience with coding, so ...
1
vote
2answers
572 views

Problem with boundary values for a partial differential equation

I have a PDE problem that I can't solve. and I wonder if you could help me with it. I have a Terzaghi Consolidation equation (similar to the heat equation) that is written as follows: ...
6
votes
2answers
285 views

Catching only the first event in NDSolve EventLocator

I have a system of ODEs that I solve. During the integration process, there's an event that I want to catch, but I want to (a) continue the integration after the event and (b) catch only the first ...
5
votes
1answer
286 views

NDSolve and WhenEvent Causing Excess Work

When I use the following system model = {x'[t] == x[t] (1 - x[t]) - x[t] y[t], y'[t] == x[t] y[t] - y[t], x[0] == 0.5, y[0] == 0.5} with the ...
3
votes
2answers
150 views

Evaluate an ODE for several values of a coefficient and draw all the solutions in one plot

I want to draw one plot showing all the solutions the following ODE with different values of N. How can i do it? ...
10
votes
2answers
192 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 ...
1
vote
1answer
674 views

How can I understand the result Mathematica returns from DSolve?

I have solved an ODE using DSolve, but I have a problem with understanding the solution. In general the solution is in the form: ...
4
votes
1answer
333 views

Eliminating functions from system of PDE in Mathematica

Mathematica users, Let's see an example of three PDEs: How can I eliminate variables q1[x,y,z] and q2[x,y,z] from a system of ...
7
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
726 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
563 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
748 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
189 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
213 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
148 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
305 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
310 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
509 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
1k 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
374 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 ...
6
votes
2answers
1k 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
867 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
237 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 ...
14
votes
3answers
11k 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
5k 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 ...
4
votes
1answer
924 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
1k 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
294 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
393 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
216 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
641 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
373 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 ...
4
votes
3answers
538 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
386 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
198 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
628 views

No result from DSolve

I don't get any answer when I evaluate the following expression: ...
2
votes
1answer
343 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 ...
3
votes
1answer
1k 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
533 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
293 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
662 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 ...
10
votes
3answers
3k 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
629 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
490 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 ...
6
votes
2answers
4k 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
434 views

Second Order Non Linear Differential Equation

I'm trying to solve the following differential equation numerically: ...