Questions on the use of numerical functions NIntegrate and NDSolve.
3
votes
1answer
408 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
319 views
How to use NDSolve to track a deviation from equilibrium?
i have a task to find a event, to achieve this i think need to integrate until a constant function suddenly breaks the equilibrium and give a sharp peak.
I think that EventLocator should work, thus ...
3
votes
1answer
115 views
Integrating over data points from an external source (wolfram|alpha and weather)
I moved to another city and the weather sucks.
Sometimes I feel like getting sad and so I go to wolfram|alpha and check for example
${}$
...
3
votes
1answer
198 views
NIntegrate error bound
I am trying to evaluate a highly oscillatory integral using NIntegrate. I fear that due to limited resources (time and/or memory), I will not be able to evaluate the integral to the desired precision. ...
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 ...
3
votes
1answer
149 views
3
votes
1answer
55 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
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
304 views
Second Order Non Linear Differential Equation
I'm trying to solve the following differential equation numerically:
...
3
votes
1answer
251 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
62 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
110 views
Principal Value Integration with NIntegrate [closed]
While trying to integrate numerically a function involving singularity (triple pole) I encounter some strange behaviour of Mathematica (I'm using Method -> "PrincipalValue"). Maybe someone can explain ...
3
votes
0answers
225 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
360 views
Solving a system of nonlinear equations self-consistently
I am trying to solve a set of three non-linear equations in Mathematica. I need help with them. The Mathematica code (in plain text format) is attached below. If you copy & paste the code below ...
3
votes
0answers
406 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
101 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
202 views
Area or NIntegrate curves defined by points?
Is there a convenient method to compute the AUC (Area Under the Curve) metric that quantifies a Receiver Operating Characteristic (ROC) like shown here?
The data used to build the ROC are just ...
2
votes
1answer
214 views
Creating hexahedral finite elements in Mathematica
Is it possible to do FEM using hexahedral elements in Mathematica? If it possible, is there any help to do that?
2
votes
1answer
52 views
NDSolve with vector function
(Possible duplicate yet I still can't understand.)
Basic 2D revolving around origin:
...
2
votes
2answers
185 views
Problem with setting working precision in NIntegrate
I want to obtain a good numerical approximation (up to 10 decimal place would be ok for me) to an integral:
$$
\int^{\infty}_{0} f(r)r^2dr
$$
I am using the function $f(r)$, which is related to the ...
2
votes
1answer
208 views
Differential equations with jump conditions
Suppose I want to solve an ODE with a DiracDelta source term. In the following example, DSolve does it correctly while ...
2
votes
2answers
162 views
Animating the Lorenz Equations
I am trying to use the Animate command to vary a parameter of the Lorenz Equations in 3-D phase space and I'm not having much luck.
The equations are:
...
2
votes
2answers
259 views
NDSolve: Normalizing at every step
Suppose I have an transport equation with an initial conditions:
...
2
votes
1answer
46 views
Numerical integration with OwnValues
Say I have a symbol with an OwnValue
a = y
And we define an integration like this
...
2
votes
2answers
167 views
Making NIntegrate behave like a listable function
I have a function defined by
$$f(t)=\int\limits_0^t g(x) dx$$
$g(x)$ is a complicated function (specifically the Mittag-Leffler function which has recently been implemented in Mathematica 9 as ...
2
votes
1answer
136 views
Singular integral: NIntegrate fails to converge
I need to calculate the following singular integral:
NIntegrate[Log[1 + y^2]/Cos[Pi y], {y, 0, 1}]
However, it is failing to converge. I have tried to specify ...
2
votes
1answer
215 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
2answers
68 views
2
votes
1answer
64 views
Infinite Expression Error from NDSolve
I am trying to solve a differential equation numerically. So I have
...
2
votes
2answers
293 views
Problem with NDsolve for a system of equations
I want to solve a system of differential equations which is not very complicated, but I cannot handle the problem with mathematica!!
Please have a look at the problem and result and help me with your ...
2
votes
1answer
588 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 ...
2
votes
1answer
99 views
Differences between ParametricPlot3D and NIntegrate
I have a function $f : \mathbb{R} \rightarrow \mathbb{R}^3$ defined in a rather nasty way in mathematica however it's a smooth function and what not. I am interested in $f'[t]$ and when I run it ...
2
votes
1answer
201 views
Calculating volume [closed]
I'm new in mathematica and I'm stucked on how I can get the volume of a solid created by the inequation:
...
2
votes
1answer
145 views
how to nest parallelized computations on a cluster?
I am lucky to have access to a computational cluster and I could submit my job to many-many cores. As I need to evaluate a numerical integral within a numerical integral, I would like to know if I can ...
2
votes
0answers
78 views
Solving homogeneous Fredholm Equation of the second kind
I am trying to solve a homogeneous Fredholm integral equation of the second kind, i.e.
$\lambda y(x) = \int\limits_a^b e^{i[\phi(t)+k(t-x/M)^2]} y(t)\,dt$
where $\lambda$ is the eigenvalue (to be ...
2
votes
0answers
31 views
NIntegrate/NSum with parameters [duplicate]
I'm trying to calculate a continuous integral within a discrete integral.
Something similar to this (yet more complex):
...
2
votes
0answers
152 views
Is mathematica storing information it shouldn't store?
I'm seeking to find solutions to a numerical integration with a large set of parameter combinations (basically, I'm doing a brute parameter sampling). Yet, I believe the memory of the computer is ...
2
votes
1answer
149 views
Directional derivative of SiegelTheta
I'm working on a problem where I have to integrate both the Mathematica function SiegelTheta and some of its second order directional derivatives. Using the function works well but something goes ...
2
votes
0answers
137 views
FindRoot - Speed and errors
I am using FindRoot[] to solve a complicated equation. It seems I get the correct answer even though I get errors about an ...
2
votes
0answers
190 views
Inconsistent boundary and initial conditions: BC ignored altogether
Consider the following diffusion-decay equation with von Neumann b/c in the origin and Dirichlet at the other boundary:
...
2
votes
0answers
161 views
Numerical-Symbolical Integration (Calculus)
I created a simple numeric-symbolic integration. Here you can use symbolical and numerical techniques at the same time. You can also interpolate numerical integrals.
The problem with my function is ...
1
vote
1answer
217 views
1
vote
2answers
341 views
Solving a system of ODEs with the Runge-Kutta method
I´m trying to solve a system of ODEs using a fourth-order Runge-Kutta method. I have to recreate certain results to obtain my degree. But I'm a beginner at Mathematica programming and with the ...
1
vote
1answer
75 views
Syntax for integrating over limits specified by a Table
I wish to use NIntegrate to compute multidimensional integrals. However, I don't want to manually input the limits for the dimensions. I want to store the ...
1
vote
1answer
152 views
NIntegrate is resetting my variables and not giving me a result?
I am trying to check if mass conservation holds by integrating the area under a curve but to no avail.
...
1
vote
1answer
134 views
How to plot and solve the numerical solution of a integro-differential equation
I have a integro-differential equation of the form
$y'(t) = - \int_0^t {y(t_1 )} e^{t_1 - t} dt_1, {\rm{ t}} \in {\rm{[0,10], y(0) = 1}}$
My code is:
...
1
vote
2answers
91 views
NDSolve solution for driven damped pendulum diverges
I want to solve numerically for the system of the driven damped pendulum using Mathematica. This is the second-order nonlinear equation
\begin{equation}
\ddot{x} + 2 \beta \dot{x}+ \omega_0^2 \sin
...
1
vote
2answers
287 views
Numerical Integration in Laplace domain
I need to calculate two different integrals containing a Bessel function in the Laplace domain. I have tried different kinds of quadrature but didn't have any luck. I don’t know how to help ...
1
vote
1answer
99 views
How does one specify Neumann conditions for NDSolve?
I have a series of functions defined in my notebook, and then want to use this to solve a diffusion-reaction type equation. At the moment, something like this works:
...
1
vote
1answer
71 views
Get unique values for integration limits
For an multidimensional integration I want to build up the integration limits with the following code. (the length of vars is also variable)
...
