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

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2
votes
2answers
133 views

NDSolve solution does not satisfy boundary conditions

I am trying to solve a 1st order non-linear ODE ...
2
votes
2answers
122 views

Mathematica won't plot the a function that is solved from NDSolve

I have used NDSolve to solve for a function (an angle of a triple pendulum), and now I wish to plot the derivative of that function (the angular velocity). ...
0
votes
0answers
44 views

Evaluate function gives zero while plot shows non-zero function

I have obtained two functions, f and g, as two of the solutions to a certain set of PDE's (using NDSolve). I cannot provide the differential equations here because the system is very large, but will ...
1
vote
1answer
258 views

Why my differential equations become True?

I've been trying to solve a system of nonlinear differential equation, but the conditions are a bit weird. Two of the differentials equate to the same equation, but have different boundary ...
0
votes
1answer
78 views

Misunderstanding of Function Notation

I have: sol = DSolve[{y'[t] == y[t]^2 - y[t], y[0] == c}, y[t], t]; y[t_, c_] := y[t] /. First[sol]; Then: y[t,c] Produces ...
5
votes
4answers
151 views

Numerically Simulating a Simple Differential Equation: RC Circuit

I need to learn to simulate a differential equation in Mathematica. The differential equation that I need to simulate is complicated, without an analytical solution. However, I am brand new to ...
2
votes
1answer
45 views

Breaking out of NDSolve

I am solving a coupled set of differential equations with NDSolve for 6 unknown functions of time. At a certain point in time, the system hits a singular point where the potential governing the ...
1
vote
0answers
102 views

Volterra integral equation

I have to find an approximate numerical solution for the equation $$ F(x) - \lambda \int\limits_1^{x} \text{d}s \;s^2 F(s) Z(x-s) = G(x) $$ $$Z(s) = (\psi''(1-2\ h\ i\ s)- 0.5 \psi''(1-2\ h\ i\ s))$$ ...
1
vote
0answers
87 views

Plotting phase portrait from NDSolve (i.e., must plot x'[x], where $x=x(t)$)

I'm doing a double pendulum system and I wish to plot the phase portraits for each angle. I've successfully used NDSolve to solve for each of the angles. Let's just ...
4
votes
1answer
109 views

Can anyone help me to get the solution of this first order ODE?

$\ y'(x)=-\sqrt(y(x)^3)$ with initial condition $\ y(0)=-2$. In fact, this is an example here in page 3-4 ...
1
vote
0answers
51 views

How to solve Fuzzy Differential Equations

How to solve Fuzzy Differential Equations using DSolve or NDSolve, Or Differential Equations with fuzzy number as initial conditions
1
vote
1answer
48 views

Plotting ODE solutions with two parameters

I have a system of two first-order ODEs with two parameters, a and b and I'm trying to plot the solution curve in the X-Y plane at a given initial condition for various parameter values. Can someone ...
0
votes
0answers
46 views

Solving PDE with conditions

I am new to Mathematica, so it maybe a silly question. So, I'm trying to solve the following PDE with Mathematica: $u=u(x,y)$ $\partial_x ^2 u-6\partial_x \partial_yu+9\partial_y^2u=x^2+y^2$ ...
0
votes
1answer
120 views

Help solving the following non-linear differential equation

After spending several hours exploring different options, I still couldn't not figure out how to solve the following differential equations. Any suggestions would be highly appreciated. ...
1
vote
0answers
80 views

Why is my output equal to my input?

I tried to solve a system of differential equations with the code below: ...
1
vote
1answer
49 views

RSolve works slow and does not give an analytical solution for solving high order linear difference equations

RSolve@@{{a[n]-a[n-10]==101}~Join~Table[a[i+1]==101+10i,{i,0,9}],a[n],n} I want to get the exact form of general formulas, but ...
3
votes
2answers
127 views

Turning arrowheads off

My thinking was that Arrowheads[0] would turn off the arrowheads. ...
8
votes
1answer
233 views

How can I improve speed of code that generates an orbit plot?

I am attempting to generate an orbit for the "time 2 Pi map" of a forced damped pendulum. The example comes from page 57 in the Chaos text by Alligood,Sauer and Yorke, see Figure 2.7. The code ...
1
vote
0answers
41 views

Direction Field for an Ordinary Differential Equation [duplicate]

I have found links for plot the direction field of a differential equation. For example: How can I plot the direction field for a differential equation? And: Plotting the direction field of a ...
4
votes
2answers
3k views

How to handle NDSolve::ndsz problem (singularity problem)

I have 2 second order differential equations (non-linear). The physics behind them is correct. I verified the equations many times. It is a solid pendulum with a mass-spring at the end of it. Now, ...
4
votes
2answers
137 views

Coordinate free differential forms package

I am looking for a package in Mathematica which can handle differential forms in a coordinate free manner. I am aware of several packages which do differential forms, but it seems that for all of them ...
1
vote
0answers
41 views

The use of Evaluate in NDSolve and Plotting the answer [duplicate]

I am having a bit of hard time understanding the use of Evaluate when plotting the output of NDSolve. From the documentation, I enter: ...
0
votes
0answers
67 views

Having difficulty with NDSolve [closed]

I've entered: NDSolve[{y'[x] == z[x], z'[x] == -y[x], y[0] == 0, z[0] == 1}, {y, z}, {x, 0, Pi}] The code above was copied and pasted from the Mathematic help ...
14
votes
1answer
928 views

Animation of double pendulum

Sadly, I am a completely newbie. I am studying Physics and in our theoretical physics class we got the task to solve the double pendulum using Mathematica. We just got the program, but no introduction ...
1
vote
1answer
278 views

Solving a complex-valued differential equation with NDSolve

I am trying to solve $dx/dt=\sqrt{1+(ix)^{1.8}}$ for initial condition $x[0] =-0.9877 + i 0.1563$, where $x$ is a complex variable. I would like to plot the imaginary part of the solution versus the ...
2
votes
3answers
388 views

DSolve will not apply assumption m ∈ Integers

I am trying to solve a linear second order ODE using DSolve which involves an arbitrary integer m. ...
2
votes
0answers
90 views

NDSolve and strange “nonlinear coefficients problem”

I'm stuck solving the following problem. I defined two functions as follows: $$ \varphi(\lambda) = \frac{\left((\lambda-2)^2-1 \right)^2}{4}$$ $$ \gamma(\lambda) = \varepsilon^2 ...
3
votes
1answer
66 views

System of differential equations on a directed graph

I want to use Mathematica to model blood flow through a capillary network. The approach we are using is going to be to create a directed graph, and have a system of differential equations at each ...
1
vote
0answers
56 views

Maxwell propagator problem 2D [closed]

Hi folks I`m trying to turn certain matlab code to mathematica but for some reason it doesnt really want to do it could you please assist me a bit. Thanks The matlab code is as follows: ...
2
votes
2answers
92 views

Can't use my own discontinuous coefficient within NDSolve

I want to evaluate the pendulum's motion with changing equilibrium state given by eqilValue[t]: ...
3
votes
1answer
83 views

Troubles with FindFit for ODE

I need to use FindFit for ODE with arbitary number of parameters. This code (from documentation) works: ...
0
votes
1answer
37 views

Coefficients of a DiffEq [closed]

I'm attempting a Do[] recursion on Coefficient[] with the end goal to use it to find the coefficients of an nth order diffeq. The following is a basic example of what I'm trying to do, subbing a ...
0
votes
1answer
63 views

Plotting and Analysing derivatives of solution of differential equation [closed]

Using NDSolve I found the solution for the differential equation that governs the dynamics of a simple pendulum. How do I plot the derivatives of the solution? Also, I would like to find the ...
0
votes
1answer
554 views

how to solve second order nonlinear coupled differential equations using NDSolve with hyperbolic function

i have to solve some solitons scattering through this coupled equations. i need to get two different graph, but still the graph did not come out. and also the equations quite complicated containing ...
0
votes
0answers
33 views

Finding a specific number of eigenvalues in Mathematica

I'm trying to learn how to determine a specific number for eigenvalues for a transcendental equation. For example, ...
1
vote
1answer
76 views

using Module in NDSolve

I am trying to solve a set of two wave equations where solution of first equation defines initial conditions for the second one. And I would like to use Module to define those equations as a function ...
13
votes
2answers
417 views

Neumann boundary conditions in NDSolve over nontrivial region

The problem I would like to solve involves diffusion in the following region ...
1
vote
2answers
48 views

Strange behavior of the Evaluate function

I am solving a system of differential equation whose unknown are saved under variable vec={C00,C01,C10,C11} and the solutions are saved under variable ...
1
vote
2answers
107 views

ParametricNDSolve and plotting problem

I have a problem with ParametricNDSolve: ...
6
votes
1answer
216 views

Poisson PDE using FDM in Mathematica

The problem modeled by the Poisson PDE is related to the torsion of prismatic beams and I use the Finite Differences Method. When I use Mathematica to solve it using a quadratic mesh it is working ...
0
votes
0answers
40 views

Help deciphering Neumann Value

Version 10 has an option for NDSolve called "NeumannValue" which is supposed to allow you to specify boundary conditions of the form $\vec{n} . (c \nabla u + \alpha u -\gamma) = g-q u$ but there is no ...
2
votes
0answers
78 views

Hermite method in Mathematica

When I solve the example below, in the results it is mentioned that MMA 10 has used Hermite method. I cannot find anything about this in MMA documentation. Is there nothing about Hermite method ...
2
votes
2answers
163 views

ParametricPlot3D line not smooth

Multivariate parameters appear to present a jagged appearance of integrands (using default Runge-Kutta ODE integration intervals?) in ParametricPlot3D plotting on a single argument. Higher Mesh.. ...
1
vote
1answer
88 views

Problem solving a differential equation

I want to solve the following differential equation: y''[x]+a*y[x]=-b*u[x], y[0]==0, y'[0]==0 for y(x). u[x] is a vector, ...
2
votes
1answer
59 views

Evaluate function defined by DifferentialRoot

I have the following sequence of rationals that I want to find the generating function of: ...
1
vote
1answer
50 views

Series expansion of InterpolatingFunction obtained from NDSolve

I am trying to obtain a series expansion of the numerical solution of a differential equation. I encounter difficulties going beyond first-order expansions which I believe might be due to my inability ...
2
votes
1answer
132 views

Combining Gravity Turn and Orbit Models

I have a mathematical model for the motion of an orbiting spacecraft about Earth: ...
0
votes
0answers
35 views

DSolve echoes input

I'm attempting to solve a set of coupled, non-linear ordinary differential equations using DSolve, but Mathematica simply echoes the code that I put in: ...
1
vote
1answer
621 views

Integro-differential eqn with double integral

I am looking at the following variation of a integro-differential, with y[0]=1. The output is not great, any solutions to this? ...
-2
votes
0answers
47 views

solving the heat equation

I'm trying to model the diffusion equation on mathematica, but I'm a complete beginner. So far I've managed to find the heat equation on the NDSovle examples but I'm not really entirely sure what all ...