Questions on the use of numerical functions NIntegrate and NDSolve.

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3answers
755 views

Numerical solution of a differential equation with NIntegrate coefficients

I am trying to solve a linear ODE with a variable coefficient which is given in terms of an integral I can only do numerically. That is, I have an equation of the form $$ ...
5
votes
1answer
2k views

NDSolve, Schrödinger equation, and decaying solution

I am trying to solve a Schrödinger equation for a particle hitting a step potential using NDSolve in Mathematica. Here is my code: ...
5
votes
4answers
197 views

error with NIntegrate and RegionPlot

Bug introduced in 10.2 or earlier and persisting through 10.2 or later Here's a simplified example of what I'm trying to do: ...
5
votes
2answers
1k 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) = ...
5
votes
1answer
348 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
2answers
222 views

FEM giving “ … is not a polynomial error”

Executing the program below I get the ... is not a polynomial error message. I don't have an idea why I am getting this -- any suggestions? ...
5
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2answers
152 views

Example of Integrate applying a numerical evaluation N

Here is a minimal example: Integrate[(a[1] + x)^2, {x, 1., 2.}] 2.33333 + 3. a[1.] + 1. a[1.]^2 The problem is that ...
5
votes
2answers
439 views

How to find Matano plane

I have discrete collection of data points (10 to 10^4). I want to describe them by a continuous function and find a x value z, ...
5
votes
1answer
101 views

Mathematica 10.2 is slow to NIntegrate highly oscillatory integrals

I noticed that Mathematica V10.2 is taking much longer to run my code when compared with V9. One function that seems affected is NIntegrate. For example, for a ...
5
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1answer
199 views

Why does DSolve give a different result than NDSolve?

When I try DSolve to solve a system: ...
5
votes
2answers
139 views

Initial time as parameter in ParametricNDSolve

I need a help with the function ParametricNDSolve. My goal is solve the equation \begin{array} &&\dot{x}(t) = y(t) \\ &\dot{y}(t) = x(t)-1-\varepsilon Cos(\omega t) \\ &x(t_0) = x_0\\ ...
5
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1answer
126 views

memory leaks using NIntegrate on parallel kernel

Bug fixed in version 10.2.0 I'm running a large computation in parallel and the memory usage of the parallel kernels is increasing with every iteration of the calculation. Neither ...
5
votes
1answer
193 views

Slow exponential evaluation over lists

This question,which is still unanswered, might be relevant because it involves NIntegrate over lists and it also has Exp. In ...
5
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1answer
282 views

Integration of Two Manipulatable Cylinders

Introduction I created the following code to simulate the many possible interactions between a cylindrical protein crystal and a x-ray beam during serial femtosecond crystallography. ...
5
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1answer
619 views
5
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1answer
742 views

NestList and Euler's method

I am new to mathematica and so just experimenting with various programming constructs. Recently have been looking at NestList and how I could use this to implement ...
5
votes
2answers
269 views

Integrating a list of functions

For the purpose of this minimal example, let's say we have a list of functions, like this: f[y_?NumericQ] := {NIntegrate[z*y, {z, 0, 1}], a y} I want to ...
5
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1answer
88 views

In a PDE solution let us integrate out one of two coordinates

Here is a trapezoid within which I am solving a simple Laplace equation with the Dirichlet boundary conditions set at its top and bottom: ...
5
votes
1answer
126 views

Integrate over implicit 1D region: works for algebraic but not transcendental equation?

QUESTION How come this works: NIntegrate[1, {x, y} ∈ ImplicitRegion[{x == y^3, x <= 1, x >= 0}, {x, y}]] But this fails: ...
5
votes
2answers
157 views

How to add (energy) constraint when using NDSolve to Equation of Motion

To simplify my problem, I will try and solve the Equation of Motion for a particle in a 1D Harmonic Potential. energy[x_, p_, m_, ω_] := p^2/(2 m) + (m ω^2)/2 x^2 ...
5
votes
1answer
236 views

Solution to a T+U = E equation

I needed to solve really easy differential equation (in dimensionless units): $$ \mathcal{T} (\dot{\xi}) + \mathcal{U} (\xi) = \text{const.} \equiv \varepsilon ; \quad T(\dot{\xi}) = \dot{\xi}^2 ; ...
5
votes
2answers
1k views

Calculating the area under a curve, but above a certain threshold value

so here I am with a time series of data (hours (t) and corresponding measurements (a)). ...
5
votes
1answer
954 views

How can I deal with an NDSolve::ivone message regarding boundary values?

I have a question regarding the error message: ...
5
votes
1answer
118 views

A 1D numerical integral Mathematica cannot compute, from physics

A well know result in theoretical physics is that a sum over Matsubara fermionic frequencies, i.e.: $$ S = \sum_{n=-\infty}^{\infty} h(\omega_n) \hspace{32pt} \omega_n=(2n+1)\frac{\pi}{\beta} $$ can ...
5
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1answer
259 views

Obtaining an NIntegrate error estimate

Is there a way to extract the error that Mathematica estimates when calculating a numerical integral using NIntegrate? Internally Mathematica must keep track of ...
5
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1answer
117 views

Determining the range of parameters that yield real values for a certain NIntegrate form

I have specified just one set of $s$ and $g$ values that yields a real value for the NIntegrate below. It is possible that some $s,g$ combination can give rise to ...
5
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1answer
1k views

Getting MemoryAllocationFailure from NIntegrate [closed]

When numerically calculating a double integral using NIntegrate over an infinite domain (with all options at their default), Mathematica 7 calculates my integral ...
5
votes
1answer
36 views

Exploiting symmetry makes a 2D NIntegrate harder?

NIntegrate is having trouble converging, for reasons that I don't understand. Here is a simple example. I can compute the area of the curvilinear triangle ...
5
votes
1answer
341 views

How to plot the solution of a Partial Differential Equation?

My attempt. I need to solve numerically the Complex Ginzburg-Laudau Equation (CGLE): $$ \frac{\partial A}{\partial t}=\epsilon A-(1+i\beta)|A|^2A+(1+i\alpha)\nabla^2A $$ I'm using a uniform initial ...
5
votes
2answers
770 views

Numerical Integration as Model for Nonlinear Fit

I'm trying to do a fit for parameters of a function within an integral but I'm getting errors when I try and run it. Essentially I want the following fit to work out: ...
5
votes
1answer
660 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 ...
5
votes
1answer
1k 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: ...
5
votes
1answer
378 views

Numerical solution of IVP for linear ODE with variable coefficient runs wild soon

Cross posted in scicomp.SE. A friend of mine showed me this initial value problem (IVP) for a linear ordinary differential equation (ODE) with variable coefficient: $$y''(x)=\left(x^2-1\right) ...
5
votes
2answers
506 views

NDSolve: ProcessEquations and Reinitialize with Piecewise functions

I am having trouble with using NDSolve`Reinitialize when the system consists of a piecewise function. If we define the ODE system ...
5
votes
2answers
322 views

Numerical Integration with InverseErfc

I am trying to numerically integrate an equation that involves InverseErfc (embedded in the copula defined). The equation looks like the following: $$ \int_0^T \int_0^\infty \int_0^\infty ...
5
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1answer
151 views
5
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2answers
148 views

Why am I getting different answers for an integral depending on method?

I'm trying to carry out an integral and I'm finding different answers depending on which method I choose to integrate with. I assume this has something to do with divergent pieces but I don't ...
5
votes
1answer
141 views

Finding minimum fly-by radius between Mars and spacecraft from interpolating function

I've written an interplanetary trajectory solver/plotter that plots the path taken by a spacecraft on an Earth-Mars mission, but have run into a little trouble when the spacecraft actually reaches ...
5
votes
1answer
444 views

Proper use of arbitrary number of variables

So, I'm working on a project where the number of independent variables is not fixed. Consider a problem of $N$ independent variables, $\boldsymbol{r}$. I want to perform different things with them. ...
5
votes
0answers
158 views

Numerical solution of Schrödinger-type equation in Mathematica [duplicate]

I want to solve the following differential equation numerically: \begin{equation} i\partial_{t}\psi(r,t)=\left[-\frac{\Delta}{2m}+g\left|\psi(r,t)\right|^{2}+V_{d}(r,t)\right]\psi(r,t) \end{equation} ...
5
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0answers
100 views

Modify NDSolve`StateData (if possible)

I am trying to solve a PDE that needs to be scaled constantly (refer to this). @andre suggests I modify NDSolve`StateData. Now, the problem is, I'm not used to ...
5
votes
0answers
365 views

Increase precision of custom function

I hope the title is not misleading: Suppose I have a function that is quite complicated, e.g. f[u_] := Exp[-Exp[- Abs[c.u]^a] Sin[d.u] Sin[(Abs[c.u]^a) ... I ...
4
votes
2answers
1k views

Does Mathematica have a command analogous to ode45 of MATLAB?

Does anybody know if Mathematica has an analogue of MATLAB's ode45 command? I need to solve a second order coupled ODE system of equations.
4
votes
2answers
327 views

Approximate value for the area between the curve

I've got this task: Use Mathematica to obtain an approximate value for the area between the curve $y=1/4$ and the x-axis over the interval $[1,2]$ with $50$ subintervals using the left ...
4
votes
2answers
866 views

How to solve for an Z-Score of a T-Distribution?

I'm looking for the Z-Score for a distribution, where the integrated area sums up to 0.90. Unfortunately I always get an error from Mathematica, ...
4
votes
5answers
565 views

Problem using WhenEvent to constrain solution

Note: This question has also been posted at the Wolfram Community Problem: Simulate pressure in volume 1 and 2 for 1 second. The circuit is as follows: From this I set up the governing DE for ...
4
votes
3answers
740 views

Find arc length

I am trying to find the arc length for using ...
4
votes
2answers
196 views

LevinRule and SphericalBessels

I'm currently looking at a simplified problem that approximates another problem I'm looking into. In this simplified problem I at least have an analytic integrand and can easily provide all info on ...
4
votes
3answers
555 views

How could I get the value of y[t] at each specific interpolation point?

sol = NDSolve[{Derivative[2][y][t] + Sin[y[t]] == 0, Derivative[1][y][0] == 0, y[0] == 1}, y, {t, 0, 2}] the above-mentioned differential equations can be solved ...