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

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0
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1answer
124 views

NDSolve in exact points - nonlinear equation (Degrees and Radians confusion)

I found solutions of two nonlinear equations, but I have three small questions. First I am in confusion because of initial value. The system is mechanical and unknown ϕ is an angle, which I set to ...
1
vote
1answer
137 views

Numerically solving an ODE for a parameter

My equation is as follows: sol = ParametricNDSolve[{(f'[r]^2 - 1) f'[r] r == 6.2 (f'[1])^2/1000, f[1] == a}, {f}, {r, 1, 3}, {a}] where the function ...
0
votes
0answers
230 views

Boundary Value Problem- using NDSolve or another method

I am trying to solve a set of coupled partial differential equations, with defined boundary conditions using mathematica. Here are the equations and the boundary conditions. ...
2
votes
2answers
229 views

WhenEvent for several variables

I want to solve a system of nonlinear two differential equations (say, in $\theta(x,t)$ and $\phi(x,t)$ with NDSolve, but I want to stop the evaluation when one of ...
4
votes
2answers
447 views

How to transform transfer functions into differential equations?

is there a way with Mathematica to transform transferfunctions (Laplace) into differential equations? Let's say I have the transfer function $\frac{Y(s)}{U(s)}=\text{Kp} \left(\frac{1}{s ...
1
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2answers
163 views

NDsolve with variable end-point

I want to plot the solution a coupled ODEs as a function of the end point only. Mathematica code: ...
1
vote
1answer
69 views

Invariant error plot for an arbitray system of ODE

i try to use InvariantErrorPlot command for a generic system of ODE but i find only example with pre-building equations from Mathematica Packages. This is one of ...
2
votes
0answers
92 views

Are there some other ways to solve a second PDE except DSolve?

I have a partial differential equation as follows: $$\frac{\partial p(x,t)}{\partial t}=\text{Dp} \frac{\partial ^2p(x,t)}{\partial x^2}-\frac{p(x,t)-\text{p0}}{\tau }$$ What I try to do was to get ...
0
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0answers
112 views

Question about NDSolve

Here is my code: ...
0
votes
1answer
395 views

NDSolve example - analytical vs numerical solution. How to specify initial conditions?

So, I have the following equation: y[t]^-3 == w^2 y[t]/t^2 + y''[t] where w^2 = (t0 k0)^2. Analytic solution is easy to ...
1
vote
1answer
860 views

Euler's method for system of differential equation

I need to program Euler's method to solve a system of two diffferential equations of first order. Fist, I have programmed the Euler's method for just one differential equation: ...
2
votes
1answer
171 views

The output is the same as Input when I add the boundary conditions to a PDE

I am trying to solve a PDE in the first order with specific boundary conditions. When I solve use DSolve without the boundary conditions, Mathematica gives me an answer in an arbitrary function. When ...
2
votes
2answers
545 views

How to visualize slope fields of differential equations without vectors?

I'm looking to visualize slope fields of differential equations for my differential equations course. Every example I see draws them as vectors, adding unnecessary "arrows" that, to me, are visually ...
0
votes
1answer
243 views

Initial and boundary value errors

NDSolve::ivone: Boundary values may only be specified for one independent variable. Initial values may only be specified at one value of the other independent variable. >> I keep getting this, ...
0
votes
1answer
121 views

Plotting the discrete solution to a PDE

So I went through all the grunt work of solving a PDE in discrete form for a research project. Now I have a Temperature solution as a function of time and space: $$ T_{i}^{n+1}=\left( \dfrac ...
0
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0answers
258 views

How to obtain differential equations of motion using Lagrangian dynamics?

I'm confused to find a set of differential equations of motion of a pair of masses, m1 and m2 joined by a spring of constant ...
0
votes
1answer
46 views

How do I pull from a data list for parameter values in a system of ODEs and then solve and plot?

I have a parameter set list and I would like to solve a system of ODEs multiple times using each parameter set in the list. Then I would like each set of solutions to be graphed on the same plot. ...
0
votes
0answers
140 views

Boundary Condition Problem with Green's Function

My temperature distribution looks like: Mean wire temperature is : To[x_] := 2 c1 Cosh[x a1] + a2 And it is continuous at two points. In positive part: ...
0
votes
0answers
263 views

Shooting method for solving 3rd Oder ODE with RK method

This is my 3rd Order IVP. D[y[x], {x, 3}] == (m/2)*((D[y[x], x])^2 - 1) - ((m + 1)/2)* y*(D[y[x], {x, 2}])^2. Initial conditions given are as follows ...
0
votes
3answers
442 views

Find an equations of motion using Euler Eqution [closed]

I am a completely new to Mathematica, so my question and code may look silly. I need to find a equation of motion of a point particle of mass m moving in a potential V(x) = A abs[x]^n. (n=1,2,3,4,5,6. ...
3
votes
1answer
190 views

NDSolve with varying PrecisionGoal and WorkingPrecision

Sometimes we need higher numerical precision to deal with large number cancellation in an equation. But if this cancellation happens only in a small (and known) parameter space, would it be possible ...
6
votes
2answers
725 views

StreamPlot for Bifurcation Diagram

When we do a StreamPlot, I want to show the bifurcation when $a = 0$ transitions to $a >0$, but do not see a better way to do this than the following. ...
2
votes
0answers
148 views

Internal Shooting Method of NDSolve in combination with NDSolve`Reinitialize?

To explain my problem, I am trying to extend the BVP problem example from the help that illustrates how to use the shooting method of NDSolve: ...
12
votes
3answers
1k views

Plot Matlab icon

I started to explore this on a whim and hasn't succeeded yet… Some introduction for the icon is found here but I can't understand it very well. (I admit that, though playing with ...
0
votes
1answer
125 views

Setting plot size within vector; dynamic slider (two part question)

I have a question about the size of a plot in mathematica. I'm working on some differential equations (a simplified model of heat transfer in a building). I've programmed it so that you can set ...
0
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0answers
33 views

How to Invert a Multivariate Interpolating Function? [duplicate]

I used NSolve on a partial differential equation with boundary conditions to get a numerical solution that Mathematica says is of the form InterpolatingFunction. I then defined a function f(x,y) which ...
0
votes
1answer
254 views

Infinite expression 1/0.^(1/4) encountered in NDSolve

I am trying to solve very simple system of coupled differential equations using the NDSolve function, but I am getting ...
0
votes
0answers
329 views

How to apply Robin boundary condition in Mathematica

Robin condition is the boundary condition which combines the Dirichlet and Neumann condition at the same boundary. For example: At the boundary x = 0 to 2: I want to apply ...
0
votes
0answers
150 views

Maximum of NDSolve output. Problem with interpolating function

I solve a NonLinear PDE and get a solution (which for other reasons I put into a vector): SolVec1[1][[2]][x,t], where x and t are the indipendent variables. Now, I would like to get a distribution ...
0
votes
1answer
322 views

Using NDSolve for three variables as function of time

I want to be able to plot z, and r. Should I be using DSolve, NDSolve or something else? I've tried to clear it up a bit Thanks, Will ...
3
votes
1answer
367 views

Solving Rotational Equations of Motion

I'm trying to integrate the rotational equations of motion ...
10
votes
1answer
3k views

How to solve a system of partial differential equations?

Edit: since the upgrade to Mathematica 10, this problem seems solved I just want to solve a system of partial differential equations, for example: $$ \left\{ \begin{array}{l} ...
1
vote
1answer
261 views

Boundary condition is not specified on a single edge of the boundary of the domain

I am attempting to solve a PDE as prescribed in a paper I am reading; however, Mathematica doesn't seem to be happy with the way I am posing the problem. Im my case, r(t,100) is an approximation of ...
0
votes
1answer
207 views

Cannot get specific value from NDSolve (multiple functions)

I am trying to solve six connected differential equations. This is my code: ...
1
vote
1answer
300 views

Need help with solving a second order differential equation

I need help with solving this differential equation. ...
3
votes
1answer
325 views

Solving a constrained vector system with NDSolve

I'm trying to replicate the pendulum DAE example in the Documentation Center (example/ModelConstrainedSystemsAsDAEs) using Mathematica 9's vector support with NDSolve. So far I have: ...
2
votes
1answer
497 views

Use Euler method to solve differential equation

Use Euler's Method or the Modified Euler's to solve the differential equation ${dy/dt=y^2+t^2-1, y(-2)=-2}$ on $[- 2, 2]$. Take h = 0.2 (...
2
votes
1answer
157 views

Mathematica can't find constants for this differential equation

I am having problems solving this differential equation: diffeq = m x''[t] == -a E^(b*x'[t]); sol = DSolve[{diffeq, x[0] == 0, x'[0] == v0}, x[t], t] The output ...
1
vote
1answer
223 views

Partial differential equation with initial conditions

And so I want to solve the following equation, subject to these initial conditions: $\ u_{tt} - u_{xx} = 6u^5+(8+4a)u^3-(2+4a)u$ $\ u(0,x)=\tanh(x), u_t(0,x)=0$ When I use NDSolve to solve within ...
0
votes
0answers
133 views

How to solve a ParametricNDSolve issue when the system seems to be stiff?

I have a problem with ParametricNDSolve[]. Mathematica gives the warning that a stiff system is suspected. I have varied the methods but unfortunately I was not ...
5
votes
3answers
315 views

Kinetic Friction in Mathematica, weird behaviour

I found the behavoiur of Sign function weird in the code below. when $T=10$ ...
1
vote
1answer
242 views

Looping with NDSolve?

I have a series of PDE equations that are solved with NDSolve for certain variables $a$ and $b$ - Now, I want to see the output at a time $t$ as $a$ and $b$ change; so I was thinking of a loop ...
1
vote
0answers
207 views

Complicated condition for system of differential equation

I am trying to solve a series of nonlinear differential equation with complex condition as described by block diagram below. The left figure describes general concepts and the right figure describes ...
2
votes
1answer
380 views

How to use Compile with NDSolve function for large no of differential equations?

Matrix M[t] and and Hamiltonian of same order L^n x L^n. ...
4
votes
1answer
264 views

How to choose MaxStepFraction for optimal speed of NDSolve

I'm trying to use NDSolve to solve a 1D Schrodinger's equation, and it seems that MaxStepFraction has huge effect on the ...
0
votes
1answer
119 views

Problem with Plot of Solution for NDSolve [closed]

I'm trying to plot the solution of an equation using NDSolve. For some reason nothing shows up in the plot. I checked the output of the interpolating function and it doesn't look like there is ...
2
votes
3answers
250 views

Differential equation of a physical property which can not be below zero

A simple question but maybe also interesting for others. I have the simple differential equation: a'[t] == -r The quantity a has a physical meaning and can not ...
0
votes
1answer
144 views

Piecewise of different functions

You know, NDsolve coupled with Piecewise can be used to solve a series of discontinuous differential equations. But what if one of the function is different? For example: ...
1
vote
2answers
124 views

Eliminate complex answer to differential equation

I've tried the following: ...
0
votes
2answers
186 views

Asymptotic series [duplicate]

I need to solve the following problem. I have the following function: Erf[Sqrt[a x^2 + b y^2]]/Sqrt[a x^2 + b y^2], where x and y are variables and a and b ...