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

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2
votes
1answer
68 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
65 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 ...
0
votes
0answers
41 views

Evaluate result from NDSolve is slow

I am calculating some partial differential equations with NDSolve, it does it well. However when I try to Evaluate the ...
2
votes
1answer
38 views

NDSolve : Boundary conditions of lower order

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

how to change parameters in NDSolve?

I want to solve a PDE with parameters chosen based on the sign of derivative. For instance in the following PDE ...
4
votes
3answers
246 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
76 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
49 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
77 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
45 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 ...
0
votes
0answers
58 views

Two warning messages in NIntegrate and NDSolve

Everybody I am trying to replicate the Figure.7 of the article arXiv:1103.2683 However my plot is different from it, which is as follows Then we can find the differences between both figures, first ...
1
vote
2answers
60 views

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

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
125 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 ...
-2
votes
0answers
55 views

discontinuous equation [on hold]

I want too solve this discontinuous equation and plot results. Plot[{x1[t], x2[t]}, {t, 0, 10}] If M and P are function of time or constant.
0
votes
0answers
37 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
79 views

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

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
61 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 ...
-1
votes
0answers
38 views

How to solve a certain PDE [closed]

I would like to find the solutions $C(x,r)$ and $V(x,r)$ of the following partial differential equation. with the boundary and initial conditions where a and ...
0
votes
1answer
135 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
191 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 ...
0
votes
1answer
49 views

Solving a differential equation with multiple coefficients [closed]

I have a syntax problem solving a differential equation in Mathematica (10th version). The input for the equation I need to solve is as follows: ...
9
votes
0answers
66 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
69 views

Error control for NDSolve

I have a problem controlling the numerical error associated with the following non-linear ODE : ...
-1
votes
1answer
58 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
66 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
78 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 ...
4
votes
0answers
69 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
103 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
76 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
66 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
81 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
45 views

Ndsolve parametricplot

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

Transient PDE with a complex boundary condition

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 ...
0
votes
2answers
71 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
0answers
80 views

Breather Rib parametrization from given code

Please help find expressions for principal curvatures $\kappa_1,\kappa_2 $ with a convenient parameterization using Mathematica code (R. Palais/Xah Lee) given. It is tough on me to handle the PDE ...
2
votes
1answer
43 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
68 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 ...
17
votes
2answers
249 views

Getting rid of spikes in the PDE solution

Preamble: I am solving a PDE in a domain representing a rectangle 10X10 with several circular holes, say, like this one (n is the number and r is the radius of the holes): ...
2
votes
1answer
87 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 ...
1
vote
1answer
84 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} ...
3
votes
1answer
187 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 ...
2
votes
0answers
84 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
88 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: ...
6
votes
1answer
102 views

ParametricNDSolve[ ] and NMinimize[ ] in Combination

I have the following code that is used to simulate a spacecraft orbiting Mars, and uses ParametricNDSolve to vary the spacecraft's initial conditions using a parameter value ...
1
vote
1answer
93 views

How to solve a certain coupled first order PDE system

I would like to find the solution $(U,V)\equiv (U(x,t),V(x,t))$ of the following system. \begin{equation} \displaystyle\left\{\begin{array}{l} \frac{\partial U}{\partial t}+(a+b x)\frac{\partial ...
0
votes
1answer
53 views

NDSolve precision for non-linear ODE with variable initial conditions

I am trying to numerically solve a non-linear ODE with variable initial conditions, specifically it is : $$ \partial_{t}R (r,t) ^2 + 2 R(r,t) \partial_{t} ^2 R(r,t) +r^2 k(r) = 0 $$ and my initial ...
0
votes
1answer
87 views

Variable dependency…easy one

I'm brand new to Mathematica...should be an easy one. Instead of writing u[x] everywhere in the code, how do I assign the dependency early on like this: u=u[x] ...
2
votes
0answers
56 views

How to solve heat equation with Robin type conditions with NDSolve?

Could you help me please to solve following problem! I need to solve one-dimensional heat equation with Robin type boundary conditions. But Mathematica find only constant solution with no dependence ...
0
votes
0answers
71 views

How to extract the time t of an interpolated function created by NDSolve? [duplicate]

I'm working with the function NDSolve. I give it the time of integration, the time I want it to evaluate my differential equations. Sometimes, it crashes before the end of its attribuated time ; For ...
3
votes
1answer
98 views

Specifying NeumannValue for Axial load instead of transverse load (Plane Stress situation)

I am trying to simulate a bar/link element under axial tensile load. The link is of unit thickness and I may use a plane stress model. A plane stress model is an approximation that may be used for ...