Questions on the use of numerical functions NIntegrate and NDSolve.

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1answer
219 views

Numerical Integration with Variable Parameters

So I want to numerically compute the integral of a long complicated expression over a specified domain (in this case an ellipse). I know how to use a Boole function to sample within the ellipse, but I ...
2
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1answer
101 views

Differentiating a function that has NIntegrate within it

I am something of a novice with Mathematica. I have written the following code; ...
2
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2answers
118 views

Definite Integral. Perfomance problem

I have a notebook in Mathematica 4. I'm trying to convert it to use in Mathematica 9. One of the problem is the long computation of definite integral. In Mathematica 4 the result of the following code ...
2
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1answer
466 views

Differential equations: Solving a singular/nonlinear ODE using NDSolve

I am trying to numerically solve a rather horrible looking singular/nonlinear ode: A*(y''[x]/y[x])'' +y[x]^2==1 on the interval ...
2
votes
1answer
314 views

Limitations of ParametricNDSolve family w.r.t objective functions

Observation: I can see even for very simple modification in case of an scalar objective involving an definite integral in time ParametricNDSolve fails. Here is an ...
2
votes
2answers
636 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 ...
2
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1answer
154 views
2
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1answer
104 views

How to use slots and patterns to reduce repetitive calculation?

This is kind of complicated... How can we make MMa calculate values of a function before doing multiple pattern or slot substitutions? Answers to similar questions didn't cover the case where the ...
2
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1answer
56 views

NIntegrate and Interval regions

NIntegrate does not seem to like Intervals as regions. Consider the following example function defined for a parameter "a" ...
2
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1answer
84 views

StateResponse is non-deterministic

I observed non-deterministic behaviour in StateResponse. Let's look at an example. ...
2
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1answer
93 views

Finding a root of a parameterized integral

I have a function given as a parameterized definite integral: f[a_] := Integrate[BesselJ[0, x - a] BesselJ[0, x + a], {x, -∞, ∞}] I suspect it has a root near ...
2
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1answer
249 views

How to use NIntegrate in a purely numerical mode?

I have a function that is defined as the smallest root of a given polynomial. Something like this: ...
2
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1answer
162 views

Plotting Laplace's equation on an infinite domain

I am trying to plot my solution to a Laplace equation on an infinite domain. However, when I try to plot it, Mathematica just runs with nothing happening. ...
2
votes
1answer
987 views

Can Mathematica solve integro-differential equations?

I have integro-differential equations like this: ...
2
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1answer
339 views

Avoiding zero (empty set) solution with NDSolve

I'm trying to use NDSolve for a chemical kinetics equation where the rate of conversion is given by this relationship as typed in Mathematica: ...
2
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1answer
295 views

Numerical integration involving Inverse Normal CDF

I'd like to evaluate the following numerical integration using Mathematica $$ \ \int_0^T\int_0^\infty xe^{-0.04 s}g(x,s) dxds\ $$ where g(x,s) is a Gaussian copula function with say, marginal ...
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1answer
547 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 ...
2
votes
1answer
435 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. ...
2
votes
1answer
257 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 ...
2
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1answer
275 views

Using NDSolve solution as initial condition for another NDSolve

I have solved a PDE numerically using NDSolve, and I now need to be able to use that solution as an initial condition for another ...
2
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1answer
224 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
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0answers
110 views

Volterra integral equation

I have to find an approximate numerical solution for the equation $$ F(x) - \lambda \int\limits_1^{x} \text{d}s \;s^2 F(s) Z(x-s) = G(x) $$ $$Z(s) = (\psi''(1-2\ h\ i\ s)- 0.5 \psi''(1-2\ h\ i\ s))$$ ...
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0answers
48 views

Number recognition in Mathematica [closed]

Suppose that I have a number $n$ with many decimal digits of precision. What is the code to use to get Mathematica to recognize possible closed-form expressions for that number?
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0answers
89 views

Puzzling NDSolve[] behavior for PDE (smooth solution, inconsistent with boundary conditions)

Consider the following: NDSolve[{D[z[x, y], x, x] + D[z[x, y], y, y] == 0, z[x, 0] == Sin[x], z[0, y] == Cos[y]}, z[x, y], x, y] {{z[x, y] -> ...
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0answers
118 views

Solve integral equation for upper bound

I need to find the upper bound of an integral knowing the value of the lower bound and the result of the integral. Here is my function: ...
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0answers
95 views

How to specify the time variable for NDSolve

I recall that it is possible to specify which independent variable is the "time" variable in NDSolve, but I can't find it documented anywhere. Does anyone recall ...
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0answers
127 views

Global vs local adaptive integration: lattice propagator

I was doing the first exercise in the paper Lattice QCD for Novices. This is the expected result: With the default "GlobalAdaptive" method for NIntegrate it threw errors saying that the error had ...
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0answers
128 views

Slow integration of interpolating function

I have a large file with irregularly spaced data in the format: ...
2
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0answers
94 views

Constrain integration to be over real domain

I am trying to integrate the following: Integrate[(2*Cos[Sqrt[F]*z - G])/E^(D*(p + z)^2), {z, -(h/2), h/2}] I am getting solution in complex domain: ...
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0answers
103 views

Whether NIntegrate evaluation is multithreaded or not?

About MultiThread evaluation I am talking about here, see this post I am NIntegrate the function grarm[e, 3, dimension, 1, 1, 0.005]. There is matrix operation in ...
2
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1answer
392 views

Crank-Nicolson with NDSolve?

As far as I understand, the Crank-Nicolson method (a.k.a. trapezoidal method) can be expressed as a second order implicit Runge-Kutta method. It's Butcher tableau is: ...
2
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0answers
63 views

Are FEM methods integrated in NDSolve yet? [duplicate]

About a year ago there was a discussion on these forums as to whether FEM methods have already been integrated into NDSolve in Mathematica. The answer back then was ...
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0answers
43 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): ...
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0answers
257 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
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1answer
259 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 ...
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0answers
276 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 ...
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0answers
573 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: ...
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0answers
229 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 ...
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0answers
184 views

EventLocator with LSODA?

Is the EventLocator option not compatible with LSODA on NDSolve. Below is what I tried to do ...
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0answers
211 views

Integrating over a region without singularity gives an error indicating the function has singularity in that region

I have the following 2D region over which I want to integrate a function: ...
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2answers
648 views

Computing 10-dimensional volume of a 9-sphere [closed]

I'm trying to compute 10-dimensional volume of a 9-sphere with radius r using Monte Carlo. ...
1
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3answers
198 views

plotting an Integration output

How to solve this integral by Mathematica even by numerical methods (plotting the solution) Integrate[(Cos[x] - a)/(1 + a^2 - 2*a*Cos[x])^1.5, {x, 0, 2*Pi}] It ...
1
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2answers
94 views

Evaluation of a large integral

I have a complicated large integral I want to evaluate (does not have a closed form, need an approximation), but Mathematica seems to keep "Running...". Is there any way to make Mathematica use more ...
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2answers
214 views

intersection between function and plane

I try to solve a ODE system of equations and i want to plot the intersection of the 3D solutions with a costant plane. To do this i use the follow code: ...
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1answer
213 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 ...
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1answer
549 views
1
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2answers
372 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 ...
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1answer
193 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
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1answer
74 views

Computer freezes during NIntegrate[]

I have a notebook that freezes the computer every time I run it (I mean the whole computer becomes unresponsive and do not react to ctrl-shift-esc and ctr-alt-delete as well as alt-tab and ...
1
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2answers
147 views

NIntegrate piecewise vector function

Is there a way to numerically integrate a vector function defined via Piecewise? Example: ...