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

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4
votes
1answer
387 views

NDSolve problem with matrix valued function

I got a strange problem when using NDSolve to solve a matrix value function σ[t] = {{σx[t], σxy[t]}, {σyx[t], σy[t]}} when I ...
6
votes
2answers
1k views

Is it possible to do vector calculus in Mathematica?

I am trying to rearrange and manipulate some vector differential equations in Mathematica. As far as I understand you have to tell Mathematica that a variable is a vector by specifying the components ...
3
votes
2answers
239 views

How can I get WhenEvent to recognize criterion I specify?

Using NDSolve I want to solve a differential equation till a quantity which is a function of the dependent variables reaches a certain value. My functions and criteria are complicated, but I am able ...
0
votes
1answer
120 views

Differential Equation help

I have a differential equation that looks like this: ...
1
vote
2answers
198 views

Discard ODE singular solutions with Mathematica?

The solution for a homogeneous second order linear ODE is generally a constant times one function plus another constant times a different function. Sometimes one of the solution functions is ...
0
votes
1answer
449 views

Setting boundary values of a second order differential equation

Not sure what is wrong with the boundary conditions for this problem: ...
0
votes
1answer
189 views

Subtracting results of NDSolve

I have 2 variables as a results from the NDSolve[] which are ua and uw. This is how I do it, ...
16
votes
4answers
738 views

How to splice together several instances of InterpolatingFunction?

I have a set of InterpolatingFunction returned by NDSolve which are valid over different (but overall continuous) domains. How ...
12
votes
4answers
826 views

How do I solve a PDE with a strange boundary condition?

How do I solve the PDE with boundary value like this $$u(t,x,y)=0, \textrm{when } F(x,y)=0$$ using DSolve? As a specific example, I want to solve heat equation $$\frac{\partial u}{\partial ...
2
votes
1answer
226 views

Using NDSolve solution as initial condition for another NDSolve

I have solved a PDE numerically using NDSolve, and I now need to be able to use that solution as an initial condition for another ...
0
votes
1answer
505 views

How to understand and use DSolve solution

This equation is simple to DSolve in Mathematica, but I don't know how to use and understand solution. ...
4
votes
2answers
1k views

How do I plot a solution of a differential equation?

I am having trouble generating a plot for a solution to my differential equations. I always end up with just blank axes. ...
1
vote
1answer
183 views

How to transform equation

Is there any possible way to write this equation of 4th order as a system of two diff equations of second order with two new variables and to do that automatically? statespace command is transforming ...
4
votes
1answer
459 views
5
votes
0answers
344 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 ...
1
vote
1answer
179 views

Finding parameters for first positive root of solution to differential equation to be equal to a desired value

I have a differential equation with parameters. The objective is to vary the parameters such that the first positive root of the solution is equal to a desired value ...
0
votes
1answer
364 views

DSolve output - understanding how to extract result

I'm a little confused with how to use the output from DSolve. The following works ...
0
votes
1answer
627 views

Decoupling system of differential equations

Here I have one task and it is preparation for small exam. I solved it by hand for first case 1), but I need to check it in $Mathematica$ and to try to implement it for both cases 1) and 2) ...
10
votes
1answer
543 views

NDSolve Differential Equation Error

I am trying to solve the following differential equation- ...
0
votes
1answer
382 views

Boundary Value Problem

I have to solve this boundary value problem: $$\frac{\mathrm{d}e_{3x}}{\mathrm{d}l}=(M_0+F_{0z}x-F_{0x}z)e_{3z}$$ $$\frac{\mathrm{d}e_{3z}}{\mathrm{d}l}=-(M_0+F_{0z}x-F_{0x}z)e_{3x}$$ ...
1
vote
1answer
250 views

Solving the wave PDE using the Fourier method

I am trying to solve the wave PDE using the Fourier method and I need to animate the plots of the partial sum of order 45 -- U45(x,t) with initial conditions U45(x,t0), {t0, 0, 12, .2}. I am ...
3
votes
1answer
2k views

How can I solve this PDE with initial conditions?

I wish to solve the following second order partial differential equation $$u_{tt}=c^2 u_{xx}$$ with the initial conditions $$u(x,0)=e^x,\quad u_t(x,0)=\sin x$$ In Mathematica, I evaluated the ...
2
votes
0answers
545 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 ...
1
vote
1answer
422 views

Optimizing the fitting of Ordinary Differential Equation(NDsolve) involving interpolation functions

I am a newbie to this forum. I am trying to use NDsolve to solve some ODEs involving the interpolation function. Then, I will compare the fitted curve and data to determine the ODE coefficients. ...
0
votes
0answers
96 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)] ...
-1
votes
1answer
168 views

Some Problem with WhenEvent!

Anyone knows what's the problem with the following code and how can I fix it? I am not sure that I wrote the WhenEvent section correctly. By the way, I want to solve the equations and then plot y vs. ...
4
votes
3answers
1k views

Lyapunov Exponent

Does anyone know a (simple) Mathematica code for computing the Lyuponov Exponent for the Rossler System? Thank you Rossler System: ...
4
votes
0answers
108 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
1answer
780 views

How to correctly use DSolve when the force is an impulse (dirac delta) and initial conditions are not zero

DSolve (and NDSolve) return different and unexpected solution to differential equation when the input is an impulse. This is ...
1
vote
1answer
308 views

NDSolve for PDE with discontinuous initial/terminal condition

I have an issue with NDSolve for the case of a PDE with discontinuous initial/terminal condition. Consider the PDE solution ...
3
votes
1answer
780 views

Lorenz map for the Rössler system [duplicate]

Possible Duplicate: How to find all the local minima/maxima in a range I have the solution of the following non-linear system: ...
5
votes
1answer
241 views

How do I interpret an error message from DSolve?

I am trying to find non-trivial solutions of the ODE $\lambda u'(x) = u(x+R) - u(x)$ using Mathematica. In particular, I am using the command ...
1
vote
2answers
458 views

NDSolve problems of convergence

I have a big function that I have to maximize, so I have to evaluate some equation with thousands of different values of the parameter. But the FindMaximum returns me many errors. I have traced the ...
0
votes
1answer
290 views

Problem with #1's in DSolve

I've entered the following functions into my notebook, but the solution to them contains #1's that I can't seem to make any sense of. The functions are: ...
0
votes
1answer
199 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
542 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
274 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
285 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
149 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
170 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
639 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
325 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
1k 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
711 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
534 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 ...
6
votes
3answers
717 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
183 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
211 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
145 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
296 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 ...