# Tagged Questions

Questions on the use of numerical functions NIntegrate and NDSolve.

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 ...
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 ...
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 ${}$ ...
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. ...
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 ...
1answer
149 views

### NIntegrate inside NSum

Consider the following function with a numerical integration: ...
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 ...
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 ...
1answer
304 views

### Second Order Non Linear Differential Equation

I'm trying to solve the following differential equation numerically: ...
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 ...
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: ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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?
1answer
52 views

### NDSolve with vector function

(Possible duplicate yet I still can't understand.) Basic 2D revolving around origin: ...
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 ...
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 ...
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: ...
2answers
259 views

### NDSolve: Normalizing at every step

Suppose I have an transport equation with an initial conditions: ...
1answer
46 views

### Numerical integration with OwnValues

Say I have a symbol with an OwnValue a = y And we define an integration like this ...
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 ...
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 ...
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: ...
2answers
68 views

### Strange Behavior of NDSolve

I am trying to evaluate the following ODE numerically: ...
1answer
64 views

### Infinite Expression Error from NDSolve

I am trying to solve a differential equation numerically. So I have ...
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 ...
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 ...
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 ...
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: ...
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 ...
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 ...
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): ...
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 ...
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 ...
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 ...
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: ...
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 ...
1answer
217 views

### Why does this numeric integral fail to converge?

I have an integral over a region (rpp): ...
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 ...
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 ...
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. ...
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: ...
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 ...
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 ...
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: ...
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) ...
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