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

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1
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2answers
81 views

Problems with WhenEvent

Any help/explanations will be highly appreciated: This works: ...
0
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0answers
19 views

How can I obtain absolute result for Root[ # ] symbol [duplicate]

I'm using mathematica 8.0. When I calculate NDSolve`ImplicitRungeKuttaGaussCoefficients[10, Infinity] function, it gives me some symbolic results. I trided //N and //FuıllSimplify operation as in How ...
4
votes
2answers
283 views

Finding a 3d curve from torsion and curvature with NDSolve

I'm trying to use the Frenet–Serret formulas to find the curve that matches the torsion and curvature I specify numerically with an InterpolatingFunction. The ...
1
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0answers
64 views

No response from DSolve

Using optimal control theory, I am trying to find the optimal paths of d and k such that they will maximize profit as given by lc: ...
2
votes
1answer
171 views

Resonance Curve using NDSolve

I am trying to make a resonance curve like this one below, using NDSolve. I tried to use code as below. Basically I try to hold solution for a w (driving frequency value) using NumericQ and then ...
2
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0answers
44 views

Understanding NDSolve::ndsz

I'm working on a largeish system of differential equations where I encounter the NDSolve::ndsz step size is effectively zero; singularity or stiff system suspected ...
2
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3answers
583 views

Plotting heat equation in a Manipulate expression

I have a 2D heat equation $u_t = \alpha (u_{xx} + u_{yy})$ with conditions: $u(x, y, 0) = 300$, $u_y(x, 0, t) = \mu_1(x)$, $u_y(x, 1, t) = \mu_2(x)$, $u(0, y, t) = \mu_3(y)$, $u(1, y, t) = ...
0
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0answers
97 views

Second-order DSolve overdetermined with only 2 boundary conditions

I was going through some circuit analysis problem and came up with a second-order differential equation, which I decided to solve with Mathematica: $$ L\frac{\mathrm{d}^{2} I}{\mathrm{d}t^{2}} + ...
0
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0answers
127 views

“Hard” ODE with three kind of solution: IVP or BVP?

I want to solve numerically the second-order differential equation proposed by Coleman in this paper (equation 8, page 1804): $$ \gamma(\lambda) \lambda_{zz} + \beta(\lambda) \lambda_z^2 + ...
1
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0answers
141 views

DSolve 2nd Order Coupled Partial Differential Equations

I am trying to use Mathematica to solve 2 coupled differential equations. My equations are of the form \begin{equation}\ddot{x}_i + A_{il} \partial^l A^{jk} ( \dot{x}_b \dot{x}_c - y_b y_c ) =0 ...
0
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0answers
103 views

Solving simple ODE for eigenvalues causes nightmares

I had some code which could solve an ODE for the function $u$ and the eigenvalue $E$. Unfortunately, $E$ is a function of another parameter $k$. This meant, that upon solving the equations, I had to ...
0
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0answers
150 views

Crank-Nicolson scheme for Schrodinger equation

I try to solve 1D Schrodinger equation with Crank-Nickolson methode. I use atomic units: time < 10^-14 => 413 a.u.t. length 30 * 10^-9 m => 567 Bohr radii ...
9
votes
1answer
289 views

How to solve a stiff nonlinear second-order ode?

I want to solve a nonlinear second order ODE as an initial value problem (IVP). Unfortunately, for certain values of first derivative at starting point I get a stiff-problem. I tried to overtake this ...
0
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0answers
75 views

Issue with NDSolve

This could be a stupid issue, but I have been checking for ages. I cannot solve this apparently innocuous system of PDEs: ...
5
votes
1answer
212 views
5
votes
2answers
187 views

Manipulation of InterpolatingFunction

Suppose that $q[t]$ is obtained by NDSolve as an InterpolatingFunction, and I want to define $Q[t]$ to be some function of ...
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1answer
116 views

Can anyone help to solve this set of coupled ODE? [closed]

After some time Mathematica just give me the same thing while I was trying to solve: DSolve[{3 E^(-[Lambda]2 [Phi]0) r a[r] - 1/2 [Lambda]1 [Phi][r] + 3/8 E^(-[Lambda]2 [Phi]0) [Lambda]1 ...
1
vote
1answer
179 views

Plotting equations of motion of a baseball

So I went through the physics of a baseball and I got the exact same equations as shown here on page 8. I input all of the same parameters into my code, and I don't get the same thing. Any idea ...
0
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0answers
79 views

Reading Eigenvalue / Eigenfunction result from Reduce

I am trying to find the eigenvalue/eigenfunction solution to: $$\tag 1 y''+3y + \lambda y=0 ; y'(0)=0, y'(\pi)=0$$ I used DSolve and Reduce and they seem to converge, however (embarrassingly) I am ...
4
votes
1answer
114 views

Ordinary differential equation invloving the function composition

I want to solve the following function: DSolve[(A1*Exp[B1*f[x]] + A2*Exp[B2*f[x]])*f'[x] == A1*Exp[B1*x] + A2*Exp[B2*x], f[x], x] And this is what I get as an ...
3
votes
1answer
87 views

NDSolve`ImplicitRungeKuttaGaussCoefficients doesn't work

I am using Mathematica 9.0 on Ubuntu. I tried the first example from this documentation page, but it returns unevaluated: ...
0
votes
3answers
257 views

Solving a differential equation with mixed conditions using DSolve

I want to solve a differential equation $$ \frac{d}{dx}\left(k_0 \left(\frac{T(x)}{T_0}\right)^n \frac{dT(x)}{dx}\right)=0,$$ with boundary conditions: $T(l)=T_0$, $\;T'(0)=-\frac{q_0}{k_0 ...
4
votes
5answers
332 views

Problem using WhenEvent to constrain solution

Note: This question has also been posted at the Wolfram Community Problem: Simulate pressure in volume 1 and 2 for 1 second. The circuit is as follows: From this I set up the governing DE for ...
7
votes
0answers
280 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
77 views

Will I be able to use NDSolve, and then how

So I am completely new to Mathematica, so sorry if this is a dumb question. I have a set of 3 coupled nonlinear differential equations. They are (a,b,c,D,L constants): ...
0
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0answers
57 views

How to solve initial value problem using Runge-Kutta method? [duplicate]

How to solve the following initial value problem using Runge-Kutta method u''[x] + (2/x) u'[x] + E^(u[x]) == 0, u[0] == 0, u'[0] == 0
0
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1answer
93 views

Solving NLODE with substitution

I am trying to get a solution to a non-linear ODE, below is the code that works for my problem. ...
1
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0answers
204 views

Differential equations: How do I solve a delay differential equation with 0-1 variables

How do I solve the following non-linear, delay-differential equations using Mathematica under the assumptions $$p(t) = 1 ,\; y(t) > k$$ $$p(t) = 0,\; y(t)<= \ k$$. $$ \frac{dw}{dt} = ...
10
votes
2answers
145 views

Return partial result when MemoryConstrained aborts NDSolve

I use NDSolve to solve a large set (~400) of coupled ODEs. Sometimes, the memory (~4GB) gets filled up, and my computer becomes impossible to work with, because it ...
3
votes
1answer
97 views

Nested NDSolve with WhenEvent: setting up new equations and discarding old ones

I am checking a complex situation where a function x1[t1] only exit in a finite time span, and after this a new function x2[t2] ...
0
votes
0answers
110 views

Dsolve not working

I am new to using DSolve. In trying to solve a differential equation I was getting nonsense from Mathematica, so I tried to solve an even easier equation ...
8
votes
2answers
464 views

Can Mathematica solve this sort of functional/differential equation?

I am looking for differentiable functions $f$ from the unit interval to itself that satisfy the following equation $\forall\:p \in \left( 0,1 \right)$: $$1-p-f(f(p))-f(p)f'(f(p))=0$$ Is there a way ...
8
votes
2answers
269 views

How to make use of an interpolating function outside of Mathematica? [duplicate]

I'm currently working on a project where I have to solve some partial differential equations. Initially, I made some approximations so that an analytic solution could be obtained, and my ...
7
votes
1answer
226 views

Inconsistent results of second derivative of inverse fourier transform

I am trying to get the Green's function of a toy diffusion equation $$\frac{\partial^2 u(x,t)}{\partial x^2} = \frac{1}{\alpha^2}\frac{\partial u(x,t)}{\partial t}$$ with Mathematica 9. Then solve ...
1
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0answers
115 views

Plotting basin boundary

How to plot the basin boundary in Mathematica? I have been trying to do this using the system ...
4
votes
0answers
233 views

NDSolve: ProcessEquations and Reinitialize with Piecewise functions

I am having trouble with using NDSolve`Reinitialize when the system consists of a pieceise function. If we define the ODE system ...
1
vote
2answers
130 views

Plot the velocity

So I am trying to find the connection between Forcing Amplitude and Velocity in a differential equation (Which is the part of system of differential equations). Those system differential equations ...
0
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1answer
106 views

Bifurcation with a system of equations

I'm trying to plot a flip bifurcation diagram for a dynamical system of equations as follows: x'[t] == v[t] v'[t] == x[t] - A x[t]^3 + R*Cos[\[Omega]*t] - B v[t] ...
5
votes
3answers
389 views

Solving recurrence sequence using an ODE

I'm trying to solve the recurrence a[n] == 0 for n < l a[l] == 1 a[n] == (l + 2(n - l) a[n - l] + (n - l)(n - 1) a[n - 1])/n(n - l + 1) for n >= l using ...
7
votes
1answer
392 views

Issue with the NDSolve code

With this procedure, one may determine an eigen-value function $R(a)$ for any given $\Xi$ (say 0, 25, 50, 75, 100) ...
8
votes
1answer
241 views

how to simplify large expression with lots of special functions in it (BesselY, Hypergeometric, MeijerG etc…)

I saw this DE in Maple forum. When solving it using Mathematica 9.01, even though the result was correct (both solutions gave the same numerical answer for some random values), Mathematica's answer ...
-2
votes
3answers
158 views

Plotting DSolve results

I am attempting to make a plot of the solution an ODE. I want to plot the solution using PolarPlot, x is the polar angle in ...
0
votes
0answers
87 views

Smoothing a function

NDsolve gives me a solution to a certain NL PDE. I want to evaluate the rate of exponential decay of the maxima of the solutions in time. So, I plot ...
0
votes
1answer
130 views

Why the result by hand is different from the command “DSolve”?

Yesterday,I use the Mathematica to solve a Differential Equation by the command DSolve: DSolve[y''[x] + 2 y'[x] + 5 y[x] == x Cos[x], y[x], x] {{y[x] -> E^-x ...
2
votes
1answer
295 views

NDSolve complains about missing derivatives of dependent variables in Mathematica 9

In Mathematica 8 NDSolve[{x[t] == 1, x[0] == 1}, x[t], {t, 0, 10}] solves fine and returns ...
0
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0answers
110 views

Linear Stability Analysis Routine. Normal Modes in NDSolve

I want to make the linear stability analyis of a nonlinear system of PDEs. So for example then I want to plot what happens to the amplitudes of the modes. To do that I need to solve my equations with ...
4
votes
1answer
121 views

WhenEvent method with 3 conditions

I am trying to solve system of differential equations below $$x''(t)=-2.25cos(1.5t)-x(t)-x'(t)$$ $$y''(t)=-1.125cos(1.5t)-4y(t)-y'(t)$$ $$z'(t)=\begin{cases}x(t)-(1+y(t)), & \text{if } ...
3
votes
0answers
141 views

Numerically solving a system of PDEs where one function is composed with the other

I'm trying to solve the following system using NDSolve: $$ \begin{align} u_t(x,t) &= u_{xx}(x,t) - v(x,t) \\ v_t(x,t) &= u(v(x,t),t) \end{align} $$ with ...
1
vote
1answer
200 views

Solving a system of non-linear differential equations

I want to solve the system of non-linear differential equations given below numerically. $$y''(t)+500y'(t)+100y(t)=-33\cos(500t)-66\cos(1000t)$$ $$300x'(t)=1000y(t)+500y'(t)-35\tanh(50x'(t))$$ ...
0
votes
1answer
95 views

Problem evaluating results of DSolve (Power::infy)

So, after browsing through older posts to see if anybody else could have had the same problem, I have come to the conclusion that I am stuck. That bothers me, especially because it should be straight ...