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

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5
votes
4answers
237 views

How should I deal with messages being produced by my Manipulate?

I have made a knockoff of John Polking's dfield for a web-embedded CDF (via Enterprise Mathematica). My code extends that from Belisarius who last year showed me how to use ...
0
votes
1answer
80 views

Problems with solving two coupled lorenz equation with NDsolve

I have a system of two coupled lorenz equations and I'm to integrate it: ...
1
vote
0answers
50 views

NDSolve error with a given system of equation [closed]

I know that my question will be very similar to NDSolve giving NDSolve::deqn: message when given my system of equations . Sorry for that, I am so new on Mathematica. I have tried to use the ...
0
votes
1answer
138 views

How to speed up NonlinearModelFit applied on a NDSolve solution?

I'm trying to perform fittings of a model defined through a system of ODEs to data consisting of time courses of a measured quantity. As described in a previous question, the system of ODEs is as ...
1
vote
0answers
230 views

NDSolve fixed step problem

Working example here: Drive folder (have both files in the same directory! Notice: the line <<variables' in the file seems to throw an error for me, but ...
3
votes
1answer
78 views

DSolve: Why does Mathematica does a separate integration from 0 instead of 1 and then from 1 to upper limit?

I am trying DSolve in Mathematica for an ODE. Here is the command I am trying and the result I get DSolve[{x'[t] + y[t] x[t] == 0, x[0] == x0}, x[t], t] $$ ...
5
votes
1answer
135 views

List of unknowns in a differential equation

I often find myself wanting to see what variables/constants are undefined in a large set of differential equations, is there a function that will do this for me? As an example, for the following ODE ...
2
votes
1answer
101 views

Fails to apply NonlinearModelFit on a numerically evaluated model defined as a system of ODEs

I call for your help with because I'm getting troubles to fit a model defined through a system of ODEs. The system of ODEs is as follows: ...
2
votes
1answer
142 views

solving coupled differential equations with parameters subject to optimization problem

I have an equation, but I don’t know how to program it in Mathematica: x[0]==1; y[0]==1; x'[t]==(a+b) x[t] y[t]; y'[t]==a b y[t]/x[t]; where ...
4
votes
2answers
274 views

NMinimize Constraints on Interpolating Functions

I have the following piece of code and am trying to use NMinimize (the last line in the following chunk of code) to minimize ...
1
vote
1answer
38 views

Reverse order in evaluated list

I solve the following set of ODE and plot solution of S1 vs k2 (Figure 1). ...
7
votes
1answer
195 views

Why should the spatial derivative order of the ODE *not* exceed two?

Following this question I came across this strange behaviour. Let me define a 1 D interval implicitely ...
7
votes
3answers
373 views

FEM Solution desired for “Plate with orifice” deflection: Application of Boundary Conditions and use of Regions

I found the deflection of an orifice plate (circular plate with a hole) subject to uniform pressure using Mathematica's NDSolve functionality. The plate is fixed at its outer circumference and is ...
11
votes
2answers
179 views

Integration of a PDE solution over a custom-defined subdomain

Preamble: In my previous question I raised a problem of a custom-chosen integration of the solution of a PDE. In that case it was an integration along a line lying within the PDE domain. The solution ...
3
votes
1answer
130 views

Increasing NDSolve computation range for 3D stationary PDE

I am trying to solve 3D Schrodinger equation (with mass equals to 1) and with no potential (I will add a potential later). My goal is to set boundary conditions on the outer boundary of a sphere and ...
2
votes
1answer
192 views

Solving SDE: $\frac{dy(t)}{dt}=(c+\sigma_wW(t))y(t)+\epsilon(t) $ in Mathematica

I want to solve this differential equation $\frac{dy(t)}{dt}=(c+\sigma_w W(t))y(t)+\epsilon(t) $. For details see ...
8
votes
1answer
206 views

SymplecticPartitionedRungeKutta shows strange error

Bug introduced in 9.0 or earlier and persisting through 10.2 or later I tried to solve Hamiltonian system ($Q$ is a vector of all generalized coordinates, $P$ - of generalized momentum) $$ ...
2
votes
0answers
44 views

NDSolve with NIntegrate [duplicate]

I'm new to Mathematica and I'm trying to use it to solve some equation like: NDSolve[x'[t]+NIntegrate[x[tau],{tau,0,t}]==20,x,{t,0,10}] But it keeps giving me ...
1
vote
1answer
63 views

Matrix issue with NDSolve

I am solving a differential matrix equation with NDSolve. ...
2
votes
1answer
117 views

Problem in understanding PDE solution

I solved the PDE shown below and I got the solution. I am new to this tool. In the solution, I have a constant multiplied by a vector like function (please refer second term of the solution). What ...
1
vote
1answer
68 views

Trouble solving a system of partial differential equations [closed]

I am trying to solve a system of linear PDEs analytically and I dont get the answer. I am new to this tool, appreciate your help ...
0
votes
1answer
94 views
1
vote
0answers
52 views

Transform a vector DE into a set of scalar DEs [closed]

I have the vector equality: {{a,b},{c,d}}.D[{x1[t],x2[t]},t]=={{e,f},{g,h}}.{u1[t],u2[t]} I want to solve this using DSolve. ...
7
votes
1answer
418 views

Dipolar magnetic field lines inside a cylinder

I'm drawing the magnetic field lines of a rotating dipole (magnetic field distorded by emission of radiation). Currently, my Mathematica 7.0 code is fully working, but I'm having a constraint which I ...
5
votes
1answer
91 views

In a PDE solution let us integrate out one of two coordinates

Here is a trapezoid within which I am solving a simple Laplace equation with the Dirichlet boundary conditions set at its top and bottom: ...
0
votes
1answer
110 views

The length of the derivative operator Derivative[0,0,2,0] in \ f^(0,0,2,0)[x,y,z,t] is not the same as the number of arguments. >>

I'm trying to solve Maxwell's wave equation but am faced with an error message ...
0
votes
1answer
62 views

Problem with solving coupled differential equations

The following code seem to produce an output that appears to be independent of the parameter "fg". It is possible that the way the code is written might be causing it, but how can one fix this ...
0
votes
0answers
43 views

Is there a way to pre-calculate a slow animation and then run easily with no lag? [duplicate]

I have an animation of a triple pendulum on a moving base, however even after trying to change the whole coding to make it faster by using module and all it is still pretty bad as I need it to be ...
6
votes
1answer
116 views

code is ignoring WhenEvent

I would like the value of x[t] to be equal to 0 when it has a negative value so I used WhenEvent but it has no effect on my code ...
-2
votes
2answers
93 views

Error in the solving of the simultaneous Ordinary Differential Equation [closed]

As I am trying to get the solution of the simultaneous ordinary differential equations ...
7
votes
0answers
210 views

DSolve returns an answer that is not a solution

Investigating DSolve misses a solution of a differential equation, I came across this odd behavior of DSolve. The following DSolve command returns an answer to the ...
0
votes
1answer
87 views
2
votes
1answer
121 views

How can I write a loop to get many values from a solution?

I am looking at the value of x[t] at day t = 200 over several years. I tried to do it using a For-loop but it didn't work. This ...
2
votes
1answer
291 views

Potential flow over cylinder with FEM: Pressure field is flipped

Much in the fashion of a few problems already answered on Mathematica.SE (1, 2), I am trying to solve the Laplace equation in velocity potential $\phi$ to simulate irrotational, inviscid flow over a ...
2
votes
2answers
166 views

NDSolve : Boundary conditions of lower order

Given the (dummy) problem ...
-5
votes
1answer
84 views

how to change parameters in NDSolve? [closed]

I want to solve a PDE with parameters chosen based on the sign of derivative. For instance in the following PDE ...
6
votes
3answers
668 views

Implementing Picard's Iteration for solving ODEs

Picard's Iteration is a way of solving the IVP $$y'(x)=f(x,y(x)), \quad y(x_0)=y_0 $$ It consists of defining the following sequence of functions recursively: $$y_0(x):=y_0 \\ ...
0
votes
1answer
158 views

How to make the plot smooth

There are some stranges point which cause the figure isn't smooth. I think that the reason is the method of numericial integration. Here is my code, it's pleasure that one can revise the drawbacks in ...
0
votes
0answers
127 views

PDE: Inconsistent equation dimensions

EDIT: I need to solve the following PDE: $\nabla^2\vec{A}=-\mu_{0}\vec{j}$ where $\vec{j}=\sigma\vec{E}$ and $\sigma=1*10^{10}$ which basically boils down to three different PDE's; ...
0
votes
1answer
105 views

How to resolve the singularity in NDSolve

I ran into a problem in my Mathematica code. There is a singularity or stiff system in NDSolve. The explicit code is as follows: ...
0
votes
1answer
103 views

Output with NDSolve

I use of the following differential equation: s = NDSolve[{y'[x] == y[x] Cos[x + y[x]], y[0] == 1}, y, {x, 0, 30}] Output. The solution in a plot. What is ...
1
vote
2answers
73 views

NDSolve giving NDSolve::deqn: message when given my system of equations [closed]

I am so new on Mathematica. I hope my question is suitable. I have looked the Documentation Center and looked also on StackExchange but I could not handle the problem. It gives always the error ...
4
votes
1answer
176 views

Unexpected results from trying to solve Laplace's equation

I am trying to find the solution to Laplace's equation: $\dfrac{\partial^2 u}{\partial x^2}+\dfrac{\partial^2 u}{\partial y^2}=0$ over the following region of space: the vertices of the triangle ...
0
votes
0answers
61 views

How do I solve first order non-linear system of PDE: $\partial f^i(x,y)/\partial z = F^i(f^1,f^2,…,f^n)$?

I've previously posted this question in Mathmatics.SE but never receive a response. The old post can be found here: ...
1
vote
0answers
337 views

How can I solve the 2D Laplace equation with Neumann boundary conditions? [closed]

I would like to solve the following boundary value problem for $u(x,y)$: PDE $\quad \quad \frac{\partial^2 u}{\partial x^2} + \frac{\partial^2 u}{\partial y^2} = 0$ Domain $\quad \quad 0 \le x \le ...
0
votes
1answer
72 views

Solving an NODE in series

How can I solve this NODE in series y''[x]^2 + (1/2)*y'[x] + (1/2) y[x] == p x + q. `p` and `q` are constant. But do not know how to actually solve it with ...
0
votes
1answer
159 views

How to solve constraint differential equations using If function

I have to solve a series of differential equations along with a constraint that has to be satisfied at each point of time where $t\in [0, 100]$ The model parameters are ...
11
votes
1answer
258 views

How to specify PDE Boundary condition on Bspline?

Context I would like to solve a PDE on a boundary which is parametrized as a BSpline. I am trying to solve the force-free Grad-Shafranov equation on a ...
12
votes
2answers
192 views

MMA breaks down when `DSolve` -ing a third-order linear ODE

My code is: DSolve[y'''[x] + (x^3 + a^3) y[x] == 0, y[x], x] It should be noted that similar code not only meets the similar problem but also returns more ...