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

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2
votes
1answer
110 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
66 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
84 views
1
vote
0answers
50 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. ...
6
votes
1answer
370 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
88 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
65 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
58 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
110 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
90 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 ...
5
votes
0answers
150 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
81 views
2
votes
1answer
120 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
231 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
113 views

NDSolve : Boundary conditions of lower order

Given the (dummy) problem ...
-5
votes
1answer
80 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
515 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
153 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
104 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
100 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
90 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
72 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
160 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
58 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
245 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
70 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
156 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
240 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 ...
11
votes
1answer
177 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 ...
3
votes
2answers
169 views

Error control for NDSolve

I have a problem controlling the numerical error associated with the following non-linear ODE : ...
-1
votes
1answer
72 views

ParametricPlot not plotting the results I'm getting from NDSolve

I try to plot a phase diagram with ParametricPlot but everytime Mathematica does nothing. I start by ; ...
0
votes
0answers
84 views

Solving a series of non-homogeneous differential equations

I have the following system of differential equations $$\rho1(t) = {(c1-\lambda(t))\over 2k1} $$ $$\dot\lambda(t)={\beta \lambda(t)-{(c1-\lambda(t))^2\over 4k1}}$$ and $$\rho2(t) = {(c2-x(t))\over ...
1
vote
0answers
94 views

How to obtain the magnetic field of the following set up [closed]

This is the experimental set up: A ferromagnetic cylindrical disk (of irrelevant dimensions) has either sides set at different electric potentials (left side at 0 volts and right side at 1 volt). A ...
5
votes
2answers
97 views

How do I programatically set up an NDSolve with lots of equations?

I'd like to set up... NDSolve[x1'[t]==2,x1[0]==0, x2'[t]==2,x2[0]==0, x3'[t]==2,x3[0]==0, x4'[t]==2,x4[0]==0, x5'[t]==2,x5[0]==0, ... etc Can I somehow use ...
6
votes
1answer
132 views

Accuracy of Grad-Shafranov PDE's NDSolveValue over implicit region

Context I need to solve for the toroidal flux of the magnetic field above an accretion disc. For this purpose, I define the region over which the flux is non zero, ...
1
vote
1answer
88 views

If[ ] not evaluating properly inside NDSolve[ ]

I am trying to solve a set of equations with the NDSolve. I encounter an error which I try to explain it with the below example. ...
3
votes
0answers
73 views

Verification of results given by NDSolve

I am trying to solve a system of ODEs using NDSolve. The differential equations used are obtained by applying method of lines to actual governing equation. The system includes differential equations ...
0
votes
2answers
99 views

Matrixform ndsolve for mobile robot dynamic equations

Error is: NDSolve::ndsdtc: The time constraint of 1.` seconds was exceeded trying to solve for derivatives, so the system will be treated as a system of differential-algebraic equations. You ...
0
votes
1answer
67 views

Ndsolve parametricplot

Ndsolve solution cant manipulate parametric plot!! ...
1
vote
0answers
76 views

Transient PDE with a complex boundary condition [closed]

I am trying to solve a PDE, but one of the boundary conditions is complex, because it includes an integral over the function that I am looking for. The code is shown below ...
1
vote
2answers
120 views

NDSolveValue and DirchletConditions for cylindrical disk

my aim in this is to model the current flow of a cylindrical disk with one end set to potential 0 and the other end set to potential 1. In this section of code I am trying to find the scalar ...
2
votes
1answer
73 views

Problem with NDSolve and Sign

If c1 cnd c2 are zero, the code responds very well; but if one of c1 or ...
0
votes
2answers
82 views

Not seeing line defined in an Epilog option

In the following code, the line defined in Epilog option of my 2nd parametric plot doesn't show up in the content pane of my ...
20
votes
2answers
395 views

Getting rid of spikes in the PDE solution

Bug introduced in 10.0 and fixed in 10.3 Note: In 10.0, Rationalize[fd, 0] was needed or mesh generation would fail. Preamble: I am solving a PDE in a domain ...
2
votes
1answer
141 views

Why does NDSolveValue giving crappy results?

I have been trying out mathematica 10 features, but sadly unable to use NDSolve for even simple PDE's. I am still wrestling with the problem of boundary conditions. The solution I get in the ...
3
votes
1answer
145 views

solving system of non-homogeneous advection equation using mathematica?

This question is followed up from this question How to solve a certain coupled first order PDE system Here I consider the non-homogeneous advection system \begin{equation} ...
4
votes
1answer
304 views

Using ParametricNDSolve and NMinimize to find accurate interplanetary trajectory arrival periapse radius

I have an interplanetary trajectory simulation that calculates the required velocity (using a Lambert solver) and escape angle for a spacecraft to travel from Earth to Mars. This model does not use a ...
3
votes
0answers
249 views

Precision and accuracy in NDSolve and NMinimize

I use NDSolve quite a lot and have noticed that setting values for AccuracyGoal and ...
3
votes
1answer
243 views

Nonlinear PDE solver

I would like to solve the following nonlinear PDE: $$ \frac{\partial^2 \phi}{\partial x^2} - \frac{\partial^2 \phi}{\partial t^2} = \lambda |\phi|^2 \phi $$ I was trying: ...