Questions on the symbolic (DSolve, DifferentialRoot) and numerical (NDSolve) solutions of differential equations in Mathematica.
3
votes
4answers
95 views
Problem with WhenEvent
I am trying to add a time dependent fraction to a parameter in NDSolve,
i.e. when 10 < t< 20, add ...
3
votes
2answers
137 views
How to remove a singularity with WhenEvent
Bellow I have a differential equation which hits a singularity at low values of t. What I want to do is somehow utilize the WhenEvent command in order to replace ...
3
votes
3answers
464 views
Lyapunov Exponent
Does anyone know a (simple) Mathematica code for computing the Lyuponov Exponent for the Rossler System?
Thank you
Rossler System:
...
3
votes
1answer
403 views
How do I find the best parameter to fit my data if the model is a interpolating function?
Hi I have a question regarding to find the best parameters for my model to fit my data.
I have 3 ordinary equation, and I now just picked some parameters (...
3
votes
1answer
402 views
Finding the Minimum value of an interpolating function
I can't seem to use FindMinValue to find the min. value of a curve represented by an interpolating function.
For instance the below code generates an interpolating ...
3
votes
1answer
409 views
Solving a PDE containing DiracDelta
I want to get the answer from a PDE:
$$\begin{align*}
\frac{\partial \rho(r,t)}{\partial t}&=Dr^{-2}\frac{\partial}{\partial r}r^2h(r)e^{-U(r)}\frac{\partial}{\partial ...
3
votes
1answer
381 views
MaxSteps and Computing time issue for Solving Differential equation in Mathematica
When we solve differential equation numerically using NDSolve then sometimes we get error like NDSolve::mxst: Maximum steps reached
According to Mathematica docs ...
3
votes
2answers
190 views
Plotting heat equation in a Manipulate expression
I have a 2D heat equation $u_t = \alpha (u_{xx} + u_{yy})$ with conditions:
$u(x, y, 0) = 300$,
$u_y(x, 0, t) = \mu_1(x)$,
$u_y(x, 1, t) = \mu_2(x)$,
$u(0, y, t) = \mu_3(y)$,
$u(1, y, t) = ...
3
votes
3answers
145 views
Mathematica not able to confirm its own solution to differential equation
I type the following into Mathematica:
DSolve[q''[x] + 2 x/(x^2 - 1) q'[x] - 4*q[x]/(x^2 - 1) == 0, q[x], x]
It gives me the result
...
3
votes
1answer
98 views
Distance between two functions satisfying a constraint
My problem is that I have two functions that are described as follows:
...
3
votes
1answer
337 views
How can I solve this PDE with initial conditions?
I wish to solve the following second order partial differential equation
$$u_{tt}=c^2 u_{xx}$$
with the initial conditions
$$u(x,0)=e^x,\quad u_t(x,0)=\sin x$$
In Mathematica, I evaluated the ...
3
votes
1answer
308 views
Bifurcation diagrams for multiple equation systems
I am interested in constructing a bifurcation diagram for some of my parameters (especially for β and γ) in the dynamical system given in the code below. I want to see how parameter changes affect the ...
3
votes
1answer
608 views
How to discretize a nonlinear PDE fast?
I wish to numerically solve the following PDE. Although there are some complete discussions for solving PDEs in tutorial/NDSolvePDE, there is no hint for the nonlinear case by discretization. Thus, I ...
3
votes
2answers
110 views
Putting NDSolve into ParametricPlot
I am having issues using Manipulate to plot the (numeric) solution to an ODE for different parameter values.
I have a code that has several stages, which seem to ...
3
votes
1answer
246 views
Eliminating functions from system of PDE in Mathematica
Mathematica users,
Let's see an example of three PDEs:
How can I eliminate variables q1[x,y,z] and q2[x,y,z] from a system of ...
3
votes
1answer
59 views
How to integrate ParametricNDSolve solution with respect to a parameter?
I have just upgraded to the new version of Mathematica because of its new built-in ParametricNDSolve function. I need to solve a first-order non-linear ordinary ...
3
votes
1answer
179 views
Tutorial for basic numerical methods for PDEs
I'm afraid this is probably not going to be a "good" question, but I'd like to use Mathematica to learn about basic numerical schemes for solving pdes. For example, I'd like to compute the solution of ...
3
votes
2answers
373 views
Lorenz map for the Rössler system [duplicate]
Possible Duplicate:
How to find all the local minima/maxima in a range
I have the solution of the following non-linear system:
...
3
votes
1answer
182 views
Construct DifferentialMatrices and Kernel for LevinRule for this integral and ODE set
I've made a lot of progress on my problem the last few days thanks to all the help I've received on here. I think I'm upto the final step of greatly improving the performance of NIntegrate[..] on my ...
3
votes
1answer
306 views
Second Order Non Linear Differential Equation
I'm trying to solve the following differential equation numerically:
...
3
votes
1answer
253 views
Efficient way to perform elementary integration step with NDSolve internal method
I'm trying to tweak the NDSolve function to perform one elementary integration step (using some explicitly selected stepping algorithm via Method option).
Such a possibility is crucial for me, since ...
3
votes
0answers
67 views
Using NDSolve for Integro-Differential Equations
I have a fairly complicated set of coupled non-linear integro-differential equations that I am trying to solve using NDSolve. The equations are:
...
3
votes
0answers
69 views
Symbolic solution to ODE, pure InverseFunction not evaluated
I'm new to Mathematica and I don't understand why in the solution of the following ODE, the #1 in the pure function is not immediately replaced by the corresponding ...
3
votes
0answers
227 views
Numerically solving PDE with high precision
I want to numerically solve the PDE
$\partial_t u(t,x)=c\partial_x u(t,x)+(mx-l)u(t,x)$
with some initial and boundary conditions and given parameters $c$, $m$ and $l$.
Consider the code
...
3
votes
0answers
410 views
How to Solve this ODE with Mixed Boundary condition
I have an ODE equation which is sort of
y''[x] + 2 y'[x]/x + .0001 (y[x])^3 ==0
subject to the boundary conditions
...
2
votes
2answers
377 views
Solution Curves and Order of Evaluation Question
I'm new to Mathematica, so I thought I'd try to exercise some solution curves.
Consider a simple first order ODE: $y'(x)=\cos(x)$. We know the solution will be of the form $y = \sin(x)+c$
I ...
2
votes
2answers
105 views
BC for transport equation using NDSolve
First I can solve a transport equation with a source (Is it still called transport equation?) using DSolve. The form of the source serves only as an example. It can ...
2
votes
2answers
211 views
Plotting several numerical solutions plus the analytic solution of ODE in one plot
I want to be able to plot several numerical solutions of an ODE plus its analytical solution in one plot in order to see how the numerical solutions converge towards the analytical one w.r.t. the ...
2
votes
1answer
110 views
ParametricPlot3D doesn't appear
Here I have one simple system solvable with NDSolve. I don't know why ParametricPlot3D doesn't present trajectory in space. I have solutions for x[t], y[t] and z[t]
...
2
votes
2answers
173 views
Weird NDSolve behavior with Piecewise (MMA9)
NDSolve in Mathematica 9.0.0 (MacOS) is behaving strangely with a piecewise right hand side. The following code (a simplified version of my real problem):
...
2
votes
3answers
268 views
How to calculate partial derivative of an unknown function
How can I force Mathematica to calculate symbolically the partial derivative of a function u[x,y] with respect to a variable ...
2
votes
2answers
598 views
Animation of Differential Equations from NDSolve with ParametricPlot3D and Evaluate
I have a system of differential equations (referred to as "s") and use NDSolve to obtain the solution. I substitute the interpolated functions for the original ...
2
votes
1answer
57 views
NDSolve with vector function
(Possible duplicate yet I still can't understand.)
Basic 2D revolving around origin:
...
2
votes
2answers
156 views
Solving and plotting ODEs while varying one of the initial conditions
How can I vary an initial condition in the numerical solution of a system of ODEs and then make a 3D plot of the solution space with that condition as one of the variables.
...
2
votes
1answer
211 views
Differential equations with jump conditions
Suppose I want to solve an ODE with a DiracDelta source term. In the following example, DSolve does it correctly while ...
2
votes
2answers
312 views
Manipulate a Differential Equation result
I want to Manipulate the result of Differential Equation like :
...
2
votes
1answer
329 views
Function output from DSolve
I want to get a function as output form DSolve.
For Example :
sol = DSolve[{Q''[t] + 40 Q'[t] + 625 Q[t] == 100*Cos[10*t], Q[0] == 0, Q'[0] == 0}, Q[t], t]
I ...
2
votes
2answers
165 views
Animating the Lorenz Equations
I am trying to use the Animate command to vary a parameter of the Lorenz Equations in 3-D phase space and I'm not having much luck.
The equations are:
...
2
votes
1answer
108 views
Plot differential equation system in a complex way
Based on this differential equation system:
$$\begin{align*}
\dot{x}&=f(x,y)\\
\dot{y}&=g(x,y)
\end{align*}$$
where
$$\begin{align*}
f(x, y)&=x^2+y^2-25\\
g(x, y)&=x^2-y^2-7
...
2
votes
2answers
259 views
NDSolve: Normalizing at every step
Suppose I have an transport equation with an initial conditions:
...
2
votes
1answer
108 views
NDSolve problem with matrix valued function
I got a strange problem when using NDSolve to solve a matrix value function
σ[t] = {{σx[t], σxy[t]}, {σyx[t], σy[t]}}
when I ...
2
votes
1answer
86 views
How to transform equation
Is there any possible way to write this equation of 4th order as a system of two diff equations of second order with two new variables and to do that automatically? statespace command is transforming ...
2
votes
1answer
219 views
How to correctly use DSolve when the force is an impulse (dirac delta) and initial conditions are not zero
DSolve (and NDSolve) return different and unexpected solution to
differential equation when the input is an impulse. This is ...
2
votes
2answers
304 views
Interpreting the interpolating function and saving data to plot with external program
So far I have been solving non-linear pdes with NDSolve and then plotting the result with the in-built Plot3D and ...
2
votes
1answer
219 views
I ran into an error when I was trying to solve a PDE with a piecewise initial condition by NDSolve
This is a very simple one-dimensional heat-conduct equation, the only special part of it is the piecewise initial condition:
...
2
votes
1answer
207 views
Laplacian or Grad of an InterpolatingFunction
For obtaining a Schlieren image from an equation for density, I need to calculate the first derivative of density and make a contour plot.
The below code snippet calculates the first derivative w.r.t ...
2
votes
1answer
70 views
Recursion depth exceeded
Below is my code for numerical solving of PDE with Crank Nicolson scheme.
...
2
votes
2answers
87 views
2
votes
2answers
84 views
Mass Symbolic Manipulation with Subscripts? (from plaintext Input)
The simplest example of the change being sought is a greek letter, typed in as plaintext nu, and its may be replaced by the symbol, ν:
expr = 3nu*kx*ky+ ...
2
votes
1answer
69 views
Infinite Expression Error from NDSolve
I am trying to solve a differential equation numerically. So I have
...
