# Tagged Questions

Questions on the use of numerical functions NIntegrate and NDSolve.

2answers
60 views

### Strange Behavior of NDSolve

I am trying to evaluate the following ODE numerically: ...
0answers
127 views

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0answers
30 views

### Precision warnings when numerically integrating a rational function from -/+ infinity [closed]

I need to integrate a function numerically from $-\infty$ to $+\infty$. Here is a condensed version of my notebook, showing the rational function and a plot of it: ...
1answer
51 views

### NDSolve with vector function

(Possible duplicate yet I still can't understand.) Basic 2D revolving around origin: ...
0answers
61 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: ...
2answers
157 views

### How to deal with zero in NDSolve in mathematica?

I would like to solve the following ODEs $$\begin{cases} x'(t)&=y\\ y'(t)&=-y(t)/t-e^{x(t)},\\ x(0)&=1,\\y(0)&=0, \end{cases}$$ (EDIT : The second equation used to be \$y'(t) = ...
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
82 views

### Getting MemoryAllocationFailure from NIntegrate

When numerically calculating a double integral using NIntegrate over an infinite domain (with all options at their default), Mathematica 7 calculates my integral ...
1answer
102 views

### DAE - varying initial conditions

I want to solve a DAE-system and I want to vary more than one initial conditions and to manipulate them. I looked here: Putting NDSolve into ParametricPlot But it does not work: ...
0answers
84 views

### NDSolve diffusion equation over/underdetermined

I have a feeling the solution to my problem is very simple… but my knowledge of differential equations is pretty weak. I am trying to solve a scalar diffusion equation (used in NMR spectroscopy, but ...
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): ...
2answers
351 views

### 3D orbits and inaccuracy over time

I wrote a little program to use Newton's Law of Universal Gravitation to animate 3 planets orbiting a central star, but I have run into a problem. Here is the code that I used to create the program (I ...
1answer
86 views

### How to adjust parameters to experimental data on a NDSolve problem

I have 2 differential equations with 2 variables, x and y,which are a function of t and I have the parameters k1, k2 y k3. ...
1answer
212 views

### Why can't I change the value of MaxRecursion in NIntegrate when integrating BesselJ?

I am trying to evaluate this integral numerically $$\int_0^{\infty } J_0(q R) \tanh(q) \, \mathrm{d}q$$ for large values of $R$. This makes the integrand oscillate more quickly and Mathematica ...
0answers
128 views

### Numerically solve 2nd order differential equation with singularity

Consider a second order differential equation with a potential that diverges at some generic value in the variable. For example: $$-y^{\prime\prime}(s)+\frac1{\mathrm{cn}{(s\mid k^2)}}y(s)=0$$ where ...
1answer
58 views

### StepMonitor not working inside ParametricNDSolveValue

Here is a toy example: ...
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
158 views

### NDSolve for a large system of simple ODEs

I am solving a system of many (more than 100) ODEs. It is the kind of standard rate equation encountered in semiconductor physics. Here is the system: ...
0answers
59 views

### Very long evaluation time of NDSolve [closed]

The following code takes a very long time, and I am not quite sure why. The Quiet is needed as otherwise there are many error messages of the form ...
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: ...
0answers
111 views

### Adapting NDSolve to circumvent NDSolve::bdord: error for 1-D Euler Equations

I attempted to use NDSolve for the 1-D isentropic unsteady flow equations with low subsonic inflow velocity and prescribed inflow total enthalpy; along with a ...
1answer
338 views

### 1D Euler Equations

Is it possible to accurately solve the 1D Euler equations in Mathematica using NDSolve? For example, let us consider the problem given here: http://www.csun.edu/~jb715473/examples/euler1d.htm Using ...
1answer
63 views

### Notation for numerical solutions to differential equations

Can somebody explain this notation to me? Using Mathematica's first example in the NDSolve documentation: ...
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: ...
2answers
132 views

### Problem with NIntegrate when WorkingPrecision is specified

I am trying to evaluate this integral numerically: $$\int_0^{\infty } m \exp (-m) J_1(m){}^2 \, dm$$ Everything is OK when only the integration method is specified: ...
1answer
64 views

### Infinite Expression Error from NDSolve

I am trying to solve a differential equation numerically. So I have ...
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
58 views

### Differentiating ParametricNDSolve solutions

Is there any way to differentiate a solution obtained by ParametricNDSolve? For instance, I have the position $\phi_\gamma(t)$ as a function of time, parametrized ...
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 ...
5answers
252 views

### How do I obtain the enclosed area of this particular parametric plot?

I'm trying to find a way to obtain the enclosed area of this particular plot. Can someone show me how? ...
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: ...
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
260 views

### Optimizing a Numerical Laplace Equation Solver

Laplace's Equation is an equation on a scalar in which, given the value of the scalar on the boundaries (the boundary conditions), one can determine the value of the scalar at any point in the region ...
3answers
144 views

### How to speed up the plot of NIntegrate?

Here is a toy example: f[t_] := NIntegrate[Sin[x], {x, 0, t}]; Plot[f[t], {t, 0, 10}] // Timing Even such a simple example will take 2.8 seconds on my computer. ...
1answer
65 views

### Error messages when using NInverseFourierTransform

I have two functions that I need to inverse Fourier transform and I was trying to get Mathematica to help me. I tried simply using theInverseFourierTransform ...
2answers
134 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 ...
1answer
132 views

### Problems with NDSolve and stiffness

I am trying to solve an ODE in chemical kinetics: $$\begin{align*} \frac{\mathrm d[x]}{\mathrm dt} &= -k_1 [x][y]\\ \frac{\mathrm d[y]}{\mathrm dt} &= k_1 [x][y] - k_3[y] \end{align*}$$ My ...
3answers
359 views

### Strategies to solve an oscillatory integrand only known numerically

I have an integrand that looks like this: the details of computation are complicated but I only know the integrand numerically (I use NDSolve to solve second ...
1answer
75 views

### NIntegrate fails while Integrate works

I have a function $f(t)$ defined as $f(t)=\int\limits_0^t(t-\xi)^{\alpha-1}\ \cos(\xi)\ d\xi$ where $0<\alpha<1$. I now want to evaluate this integral at various values of time. Therefore, my ...
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 ...
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 ...
2answers
259 views

### NDSolve: Normalizing at every step

Suppose I have an transport equation with an initial conditions: ...
0answers
128 views

### How can I speed up numerical integration of multidimensional integral?

I am numerically solving an integral equation that contains a double integral. I have managed to get a solution but it takes forever. I am wondering if there is a way to speed up numerical integration ...
1answer
144 views

### Applying l'Hôpital's Rule to NDSolve with Piecewise Function

OK, so I've been working on this problem for over a week and it's driving me crazy. I'm trying to solve a system of two differential equations in $x(t)$ and $y(t)$ using a "time-elimination method," ...
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?
0answers
81 views

### NDSolve divergence in Mathematica 9

I have been working with Mathematica 7 and 8 to numerically solve partial differential equations by MethodOfLines of NDSolve. ...
2answers
123 views

### WhenEvent in NDSolve

How come this doesn't work as I intended? ...
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, ...
1answer
117 views

### double integration

I want to evaluate a double integral, but the limits of one integral is a function of the second. Like this ...
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 ...
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