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

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9
votes
1answer
215 views

representation of custom deformation on a meshgrid

I am trying to represent 2D deformations on a rectangular grid. In Mathematica 10, there is a method to solve the elastic differential equations and then represent the deformation as presented here: ...
11
votes
3answers
3k views

Solving a time-dependent Schroedinger equation

I want to solve the time-dependent Schroedinger equation: $$ i\partial_t \psi(t) = H(t)\psi(t) $$ for matrix, time-dependent $H(t)$ and vector $\psi$. What is an efficient way of doing this so ...
13
votes
2answers
504 views

Neumann boundary conditions in NDSolve over nontrivial region

The problem I would like to solve involves diffusion in the following region ...
0
votes
0answers
39 views

How we can find shear and torsion equations for non homogeneous cross sections.? [on hold]

when we use FDM to find torsion of square section with one homogeneous material we can do it easily by mathematica "see the attached file" But what will happened if we have the same cross section with ...
0
votes
0answers
41 views

Multiply a derivative by the dependent variable

I'm fairly new to Mathematica. I want to multiply a calculated derivative by a variable, but Mathematica is not combining that correctly. ...
7
votes
1answer
159 views

Problem with Neumann condition in quarter disc

So I'm following the available examples in version 10 for FEM, The plane stress operator is shown as this ...
0
votes
0answers
39 views

EquationTrekker PropertyValue errors

In Mathematica 10.0.2, the basic example for EquationTrekker in the documentation is: ...
4
votes
1answer
228 views

Understanding of method for NDSolve

I used automatic method for NDSolve. Then I asked myself - which method Mathemathica prefered? I got an answer for this question on this forum, that I need to use: ...
1
vote
0answers
37 views

NDSolve: Equation with interpolating function [closed]

I have a question regarding DSolve and NDSolve functions in Mathematica 10. For instance, I'd like to solve an ODE: ...
5
votes
1answer
86 views

Solve a differential equation with an integral inside?

I am trying to solve this differential equation in Mathematica: y'[t]+integral from 0 to t of y[x]dx =e^(-t) where y[0]=0. Is this possible?
7
votes
2answers
234 views

Water Hammer - Numerically solving system of PDEs

I'm trying to use Mathematica to solve the water hammer effect. ...
9
votes
4answers
269 views

Should DSolve always return solution with constant of integration?

introduced in Version 10.0, fixed in 10.0.2 Clear[y,x]; DSolve[D[y[x], x] - y[x]^2 + y[x]*Sin[x] - Cos[x] == 0, y[x], x, GeneratedParameters -> C] or ...
0
votes
3answers
40 views

Error entering equation in NDSolve [closed]

NDSolve[{ 2 x'[t] + (y[t])^2/2 == t, x[t] + y[t] == Sin[t], x'[0] == -1, x[0] = 0, y'[0] == -2, y[0] == 0}, {x[t], y[t]}, {t, 0, 3}] NDSolve::deqn: Equation or list of equations expected ...
0
votes
1answer
70 views

Parametric Plotting

I am trying to make a parametric plot of the x and y displacements of a vibration problem. When trying to plot the parametric curve won't show up.
-1
votes
0answers
34 views

Plotting frequency jumps using the Duffing oscillator? [closed]

This is my input so far. I have been trying to plot hysteresis or frequency jumps by getting values for the differential equation of the Duffing oscillator, and then plot the Amplitude against the ...
0
votes
1answer
48 views

How can I assign a vector unknown function to solve the ODE system?

I noted that using non-scalar variables is convenient when a system of differential equations is governed by a process that may be difficult to express symbolically. Taking a example from the tutorial ...
0
votes
0answers
130 views

Time-dependent mesh deformation

I want to display the result of a deformation with a mesh, but I solved the deformation with a time dependency. So I have two functions: uxsol[t,x,y] and ...
-4
votes
0answers
30 views

Picard iteration method by yn(t) [on hold]

I am really bad with Mathematica, but I have an assignment due in my Real Analysis class that requires it. Here is the question: Denote successive approximations via the Picard iteration method ...
3
votes
1answer
119 views

Introduction to Vectors and NDSolve

I want to use NDSolve for a complicated equation that contains vectors. I am still new to Mathematica, and have really enjoyed what I have learned thus far. Concerning this question, I have already ...
1
vote
1answer
641 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
2answers
54 views

How to generate pure function solution using NDSolve

Suppose i have an equation NDSolve[{ca'[t]== -0.1*ca[t]*cb[t], cb'[t]== -0.1*2*ca[t]*cb[t], ca[0]== 10, cb[0]== 12},{ca,cb},{t,0,5}] how can i get the ...
8
votes
1answer
455 views

NDSolve::ndcf: Repeated convergence test failure. How to solve?

I am trying to simulate a system of $n$ pendulums with some friction in Mathematica 9. This is the code I am using: ...
2
votes
1answer
114 views

Problem solving a nonlinear differential equation with specific boundary conditions

I am trying to solve the following differential equation: DSolve[{y''[x] == A*B (y[x])^2, y'[0] == -B*C, y'[-D] == 0}, y[x], x] For my system, this ...
1
vote
1answer
62 views

Maximising solutions of NDSolve [duplicate]

I have the following system of differential equations ...
0
votes
0answers
67 views

Boundary value problem: complicated functionals

I am trying to solve a non-linear boundary value problem where the differential equation is a convoluted function of the variable I am trying to solve for. I have attached the code defining the ...
3
votes
0answers
101 views

Fractals or other patterns in the quadruple linked pendulum

This will seem like a physics question, but I'm looking for something to do in Mathematica specifically. I've successfully modeled a quadruple linked pendulum by setting up the ODEs and solving them ...
2
votes
3answers
191 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
36 views

Troubles with FindFit for ODE (elaboration)

I have asked a question Troubles with FindFit for ODE and get a good-working answer from @belisarius. Nevertheless I need to clarify is it possible to define the same model with ...
1
vote
3answers
76 views

Difficulty understanding Inverse functions are being used by Solve

I am still having difficulty with the differential equation $$\frac{dy}{dt}=y^2-y,\quad y(0)=2$$ Consider: ...
2
votes
1answer
51 views

Using NDSolve on a vector-valued PDE

I would like to use NDSolve to evaluate a PDE involving a vector valued function. For instance, I'm looking for something like a heat equation with vector-valued ...
0
votes
0answers
49 views

Plotting Poincare sections for a pendulum

Now before you direct me to this page, I'll start by saying that I'm not really using Hamiltonian mechanics to do this problem. I've already done the Lagrangian and I have solutions for both angles. I ...
-1
votes
0answers
42 views

Mathematica like dfield program

Does anyone know if a Mathematica Program exists similar to dfield written in Matlab by Dr. John Polking? http://math.rice.edu/~dfield/ D.
0
votes
1answer
47 views

How to put constraints on NDSolve[] solution

Assumed the following example of double pendulum by Thison (Answered by Jens): Animation of double pendulum Imagine that in the given animation(i.e. http://i.stack.imgur.com/p4TgL.gif ), the second ...
2
votes
1answer
78 views

2 DOF Spring Mass Damper with NDsolve and Equation of Motion in Matrix Form

I'll preface this with the fact that I have no idea what I'm doing. I'm new to Mathematica, I've only used it to solve simple ODEs with NDsolve. I'm trying to solve ...
2
votes
2answers
155 views
1
vote
1answer
265 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
84 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
3answers
183 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
50 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 ...
2
votes
0answers
108 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
94 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
111 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
56 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
52 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
54 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
123 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
85 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
50 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
131 views

Turning arrowheads off

My thinking was that Arrowheads[0] would turn off the arrowheads. ...
8
votes
1answer
259 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 ...