Questions on the use of numerical functions NIntegrate and NDSolve.
9
votes
1answer
388 views
How to tell mathematica not to resolve stiffness issues
Very often I solve partial differential equations that are nonlinear and could be up to 4th order. In these cases, it is usual for the solution determined by ...
9
votes
1answer
465 views
I failed to solve a set of one-dimension fluid mechanics PDEs with NDSolve
@DNA
The fluid here has been assumed as single component perfect gas i.e. it obeys the equation P=ρRT, the thermal conductivity is assumed as a constant, so the equation is:
...
12
votes
3answers
423 views
NIntegrating within an Ellipsoid
I need to numerically integrate an expensive positive-definite function over a 2D domain. I know by other ways that the function is basically zero for values outside the following ellipse:
...
7
votes
0answers
1k views
Integro-differential equation
I have to numerically solve a nonlinear partial integro-differential equation using Mathematica. This is my equation,
$$\frac{\partial y(x,t)}{\partial t}=\int_{-\infty}^\infty K_0(|x-u|) ...
3
votes
1answer
468 views
Methods to speed up numerical NDSolve, NIntegrate,
I am not very used to do numerical simulations on Mathematica. Do you have any ideas how to improve i.e. speed up my code?
...
8
votes
1answer
880 views
Kramers-Kronig in Mathematica
I am trying to calculate the change of the refractive index from the change of the absorption coefficient using the Kramers-Kronig relations, in Mathematica.
...
3
votes
2answers
450 views
optimization problem with NDSolve
I want to minimize the function fcc. When fcc is calculated for a specified point the answer is correct:
...
3
votes
1answer
397 views
NDSolve Problem
I am trying to solve a chemical equilibrium ODE with NDSolve where one function is the argument to another.
I.E. My equations look like:
...
7
votes
2answers
305 views
How to apply restrictions to the “integrated” variable, when using NDSolve?
I have to integrate an energy along a path. I know the energy at the "beginning" of the path (energy[0]), and I can determine the energy change (gain and loss) ...
13
votes
3answers
1k views
Solving a Volterra integral equation numerically
I would like to solve for $P(t)$, in Mathematica, a Volterra integral equation of the 2nd kind.
It is:
$$P(t) = R_0(t) + \int_0^t P(t') R_0(t-t')dt'$$
I know the function $R_0$ and would ...
11
votes
2answers
615 views
Nested NIntegrate
Suppose that we have the given simple integral expression
$$
\int_{-5}^{5} x \int_{-\infty}^{x} e^{\int_{0}^{z} -y dy} dz dx
$$
Writing this out in Mathematica we obtain:
...
3
votes
1answer
471 views
NDSolve with vectors
I'm stumped. I'm trying to write this using vectors, but the 2nd derivative isn't being expanded like I expected it to be. This is a system of equations for a projectile with quadratic drag and ...
4
votes
2answers
634 views
Is it possible to compute trapezoidal rule numerical integration?
Is it possible to compute trapezoidal rule numerical integration? I know that Mathematica has Interpolation, and that a list of points can be interpolated and then ...
8
votes
1answer
374 views
Is it possible to set a variable as a positive one in the whole notebook?
I'm having issues during integration due to the fact that Mathematica doesn't know if an undefined variable is positive or not (it gives me complexes which bothers me in the end).
For example I do ...
7
votes
4answers
330 views
2
votes
1answer
589 views
How do I prevent NIntegrate::inumr errors within other functions?
I believe this question is best illustrated with a simple example. If I run
FunctionInterpolation[NIntegrate[a + b, {a, 0, 1}], {b, 0, 1}]
I get errors of the ...
0
votes
2answers
203 views
Plotting multivariable integration
If I have a multivariable integration like
NIntegrate[x^2 + y^2, {x, 1, 5}, {y, 6, 10}]
But I need to plot its result in terms of ...
20
votes
4answers
540 views
How to use NDSolve to track equilibrium?
I am looking for an extension of NDSolve where integration runs until certain variables are settled at an equilibrium. Now I have a working solution in my sleeves ...
12
votes
4answers
1k views
Numerical Fourier transform of a complicated function
Say I have a function $f(x)$ that is given explicitly in its functional form, and I want to find its Fourier transform[1]. If $f$ is too complicated to have an analytic expression for $\hat f(k)$, how ...
5
votes
3answers
761 views
NDSolve with Euler method
I want to solve this equation with NDSolve[] using the Euler method:
x'[t] == 0.5*x[t]-0.04*(x[t])^2
with initial condition ...
5
votes
1answer
177 views
Multiple simultaneous events in EventLocator method for NDSolve
I'm using NDSolve to integrate a system of ODEs, and EventLocator to stop the integration when it leaves a certain region in phase space. This works perfectly as it should.
However, I've also added ...
15
votes
2answers
616 views
Why does Mathematica give the wrong answer when integrating?
I integrate
Integrate[Exp[I Cos[b - c]] Cos[b], {b, 0, 2 Pi}]
Mathematica gives:
2 I Pi BesselJ[1, 1]
Which is indepedent ...
6
votes
1answer
210 views
NDSolve and WhenEvent Causing Excess Work
When I use the following system
model = {x'[t] == x[t] (1 - x[t]) - x[t] y[t], y'[t] == x[t] y[t] - y[t], x[0] == 0.5, y[0] == 0.5}
with the ...
5
votes
3answers
407 views
How to use results of NDsolve[] for further solving of ODEs?
I have a system of ODEs with 10 eqns. I can solve the first 5 independently. How can I use those results to solve for the remaining 5?
An easy example would be
$\dot{x}=f(x), \quad
\dot{y}=g(x,y)$
...
11
votes
1answer
261 views
Boosting the performance of expensive NIntegrate by feeding in a cheap approximation of the integrand
I need to integrate an expensive likelihood L[x] over its n-dimensional domain.
I know that L[x] is decently approximated by a ...
7
votes
1answer
185 views
What does MaxStepFraction do?
I find that with NDSolve[...] while solving a partial differential equation, changing the MaxStepFraction from ...
6
votes
2answers
421 views
How to set the NDSolve method to LSODA
I notice that off all the Method options available for NDSolve[...], LSODA is invoked quite ...
4
votes
1answer
379 views
Solve system of ordinary differential equations that doesn't have an initial condition (t=0), but has an inifinity condition (t=infinity)?
I have a question for solving t -> Infinity on Mathematica. First, I have a system of ODEs:
...
4
votes
1answer
154 views
Could the PrecisionGoal for NDSolve be a negative number?
The help of Mathematica doesn't say so much about the PrecisionGoal for NDSolve, and I never considered much about it even after ...
2
votes
2answers
259 views
NDSolve: Normalizing at every step
Suppose I have an transport equation with an initial conditions:
...
14
votes
1answer
214 views
Why does LogLinearPlot sample its argument outside the specified domain?
I experience a weird bug in the function LogLinearPlot. If the input is an interpolation function, such as the one created like this,
...
7
votes
2answers
273 views
Starting NDSolve from intermediate time step?
I always wondered if I could start NDSolve from an intermediate time step.
What I mean is, in the code sample below, if I were to run my solution from tmin=0 to ...
7
votes
1answer
229 views
Setting the DifferenceOrder Option
I've been playing around with Method in NDSolve[...] and can't quite seem to figure out how to force ...
6
votes
1answer
207 views
Getting Integrate to perform numerical integration
I am trying to calculate the mutual impedance of two antennas which is just a big integral. I defined my function in terms of my variable, but when I execute it, Mathematica runs for a while and then ...
4
votes
1answer
249 views
Solving an ODE numerically
I really appreciate it if anyone helps me with this:
How can I solve this ODE and plot the answer for $x$ on $[0.6,5]$:
$$
\begin{align*}
-2xy'[x] = y''[x]+ 47.21 (-.0025 x^6 & + ...
3
votes
2answers
105 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 ...
2
votes
1answer
209 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 ...
1
vote
1answer
219 views
1
vote
0answers
196 views
About doing an integral
For a given integer $N$ and some function $f(x,y)$ I want to be able to do an integration of the kind,
$\int_{0} ^{\infty} \prod_ {i=1}^N da_i e^{[\sum_{n=1}^{\infty} \frac{1}{n} \left[ N + ...
1
vote
1answer
138 views
How to collect q[t] from the following integration
As shown in the following program, the q[t] in a can be collected from the integration by defining the integration of ...
0
votes
1answer
76 views
What is the correct way to use NIntegrate inside the FindMinimum function?
I'm having minor issues with the FindMinimum function when using NIntegrate inside. The functions work perfectly well but I get ...
0
votes
1answer
110 views
Nested NIntegrate - NIntegrate::inum: - error
I have the problem quite similar as in:
Nested NIntegrate
I define two functions:
...
0
votes
2answers
432 views
nested numerical integration: not valid limits?
I encountered an error when I was hoping for some Mathematica (8.0.4) magic sparing me to code up numerical integration, function approximation and root-finding myself. The broader context and the ...
