Questions on the use of numerical functions NIntegrate and NDSolve.

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115 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
896 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
178 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
661 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
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1answer
567 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 ...
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1answer
843 views

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

I have a question regarding the error message: ...
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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
70 views

Spurious infinite limit of integration message in NIntegrate

Bug introduced in 7.0 and persisting through 10.2 NIntegrate returns an error complaining that ComplexInfinity is an invalid ...
5
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2answers
446 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
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2answers
313 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 ...
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1answer
147 views
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1answer
279 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) ...
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1answer
135 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 ...
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1answer
384 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. ...
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0answers
137 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} ...
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0answers
96 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 ...
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0answers
333 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
307 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 ...
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2answers
966 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.
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2answers
1k 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: ...
4
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2answers
770 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, ...
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5answers
516 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
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3answers
604 views

Find arc length

I am trying to find the arc length for using ...
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2answers
191 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 ...
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3answers
471 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 ...
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2answers
141 views

NDSolve not returning the expected solution

I'm trying to simulate a simple circuit with Mathematica. The equation of the circuit is $R \dfrac{dQ}{dt} + \dfrac{Q(t)}{C} = f_{sig}(t)$. This is the definition of $f_{sign}$, and the function ...
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1answer
259 views

Integral of integral — it takes too much time

When I evaluate the following expression in Mathematica, it takes so much time that I don't want to wait for the evaluation to complete. So I think that there must be a better approach. ...
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2answers
128 views

Coarse-graining in numerical integrations

I have been working recently in a coarse-graining problem I found when using NIntegrate: I am trying to evaluate the function $$f(a)=\int_0^{\infty}x\,e^{-(a^2+b^2)x^2}\text{d}x$$ numerically as a ...
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2answers
315 views

How to use NIntegrate when there are symbolic constant coefficients

I would like to numerically integrate an equation such as the one below in which there are symbolic constant coefficients. I used a very simple code but it doesn't work in general, that tried to deal ...
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2answers
162 views

How to obtain the area enclosed by such a curve?

The desired curve is defined as curve02 below : ...
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2answers
138 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? ...
4
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1answer
100 views

Kernel crash when using NIntegrate with Throw/Catch

Bug fixed in 10.2.0 My code is: ...
4
votes
1answer
275 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 ...
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2answers
593 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: ...
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2answers
124 views

Postprocessing of CFD results in Mathematica

I was trying to perform computational fluid dynamics (CFD) post-processing in Mathematica after solving primitive variables from Navier-Stokes equation, mainly $(u,v)$, $(Px,Py)$. Since I am not an ...
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1answer
98 views

Does not evaluate the Integral and a plane plot

I am trying to compute a ContourPlot and a VectorPlot using the following functions: ...
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1answer
278 views

How to solve this Integral equation

D[x[t] - x[t - 1]/(2 E), {t, 3}] + Integrate[E^(-δ)*x[t - δ]/5^t, {δ, 2, 2.5}] == 0 I found solve this problem is hard with Mathematica. I also find a article ...
4
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2answers
172 views

How to plot a function that is not defined after certain point

I'm plotting a function that I get after numerically integrating over another function. Something like: f[x_,y_]:=NIntegrate[g[x,y,z],{z,0,1}] I know that above ...
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2answers
161 views

Compute the average distance from the base of a rectangular pyramid to its apex

How can I compute the average distance from the base of a rectangular pyramid to its apex? For example, if the base of the pyramid is 30 feet by 8 feet, and the height of the pyramid is 12 feet, then ...
4
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1answer
226 views

How to find derivative of a numerical solution, where precision is ambiguous?

I am trying to take the derivative of a numerical solution. I am concerned that the way I'm doing this may be problematic due to numerical error; I think there must be a better way but I'm not very ...
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1answer
422 views

Differential Equations with Matrices

I'm trying to implement the differential equation of a Cellular Neural Network in Mathematica as seen below: ...
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1answer
1k views

Incorrect solution of diffusion equation with Neumann boundary conditions

I want to set up a PDE model, which takes a two-dimensional diffusion equation into account. The key problem is that I have some trouble in solving the two-dimensional diffusion equation numerically. ...
4
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1answer
67 views

WhenEvent used in a PDE to output independent variable

I want to use WhenEvent with a PDE after it has reached steady state. I'm posting a system of 2 equations (my real system has 6) and I'm solving the advection-diffusion-reaction 2nd order PDE. First ...
4
votes
1answer
178 views

Efficient Dyson series implementation

I'm trying to implement a Dyson series \begin{array}{lcl} U(x,x_0) & = & 1 + \int_{x_0}^{x}{dy_1V(y_1)}+\int_{x_0}^x{dy_1\int_{x_0}^{y_1}{dy_2V(y_1)V(y_2)}}+\cdots \\ & &{} + ...
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1answer
319 views

Understanding of method for NDSolve

I used automatic method for NDSolve. Then I asked myself - which method Mathemathica prefered? I got an answer for this question on this forum, that I need to use: ...
4
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1answer
227 views

Find lengths of contours in a ContourPlot

I am trying to find the lengths of different contours in the following plot: It is a complicated piecewise function evaluated on the unit disk. I am hoping there is an easy, generalized way to ...
4
votes
1answer
192 views

How to do this complex integration on the real line?

$m, r$ are parameters in the following integral: Integrate[z Exp[I z r]/Sqrt[z^2 + m^2], {z, -∞, ∞}] How to do this integration directly? The result should be ...
4
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1answer
114 views

Possible bug / numerical issues with HypergeometricU — any suggestions for a fast workaround?

I've encountered some problematic behaviour with HypergeometricU. I have a probability distribution on the positive integers that takes the following form after ...