Questions on the use of numerical functions NIntegrate and NDSolve.

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47 views

Better to have infinities in limits or integrands (`NIntegrate`)? [closed]

I'm using ListPlot to plot the integral of a function with respect of the function's second variable: ...
2
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0answers
49 views

The idea behind Stiffness switching method with NDsolve [closed]

Does the Stiffness switching method with NDsolve switch just between multiple variants of 4th order Runge Kutta method or it uses also other methods?
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59 views
2
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0answers
58 views

Want NIntegrate to catch error message

Really stuck with this. When I use NIntegrate, it sometimes prints a message like NIntegrate::ncvb: "NIntegrate failed to converge to prescribed accuracy ...
2
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0answers
107 views

Problem solving a nonlinear partial differential diffusion equation [closed]

EDIT: actualy the nonlinear partial differential equations for interacting density distributions, including boundary conditions, should be given as $$ \frac{\partial\phi}{\partial t} = D ...
2
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0answers
50 views

Enforcing WorkingPrecision in NIntegrate

I have a very complicated 2D integral that I need to calculate repeatedly, and I'm trying to speed it up a bit, since at the moment it's taking a couple of days to complete. One thing I've noticed is ...
2
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1answer
158 views

How can I invoke the solution of NDSolve to determine a parameter in my equation just inside NDSlove?

I am trying to solve a differential equation by NDSlove for $h(x,t)$. It reads $$h_t=h_{xx}-V_h-\lambda(t)$$ where $V_h$ is a given function of $h(x,t)$ denoted by ...
2
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0answers
97 views

Position from 3 dimensional acceleration data? [closed]

Per a previous post on Mathematica StackExchange here I'm trying to utilize 3-axis accelerometer data to determine approximate 3D position. I wanted to start with a simple case. To this end I've ...
2
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2answers
131 views

WorkingPrecision causes issue in the NIntegrate

I really can't figure out why my code sometimes is not working. My integrals involve two variables (k and kz). The integration ...
2
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0answers
153 views

Volterra integral equation

I have to find an approximate numerical solution for the equation $$ F(x) - \lambda \int\limits_1^{x} \text{d}s \;s^2 F(s) Z(x-s) = G(x) $$ $$Z(s) = (\psi''(1-2\ h\ i\ s)- 0.5 \psi''(1-2\ h\ i\ s))$$ ...
2
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53 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?
2
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0answers
112 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] -> ...
2
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251 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: ...
2
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0answers
72 views

Nested NIntegrate of vector function

I am performing a nested integration where the upper limit of the inner integral depends on the value of the outer integral, like in the question [Nested NIntegrate]. As in this question my function ...
2
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0answers
122 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 ...
2
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0answers
169 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 ...
2
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0answers
170 views

Slow integration of interpolating function

I have a large file with irregularly spaced data in the format: ...
2
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0answers
111 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: ...
2
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0answers
117 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
493 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
67 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 ...
2
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0answers
47 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): ...
2
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0answers
282 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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0answers
331 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 ...
2
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1answer
343 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 ...
2
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0answers
317 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 ...
2
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0answers
720 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: ...
2
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0answers
191 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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218 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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1answer
744 views

Test a wooden board's vibration mode

Here is a wooden board, with dimensions shown on the picture below. How we can use Mathematica's newly build-in finite element analysis features to show the different modes of its vibrations. Assuming ...
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2answers
666 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. ...
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3answers
236 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 ...
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3answers
101 views

I know the lower limit of an integration as well as the integral. How to find the upper limit of the integration?

I used the following code. NV[x1_, x2_] := NIntegrate[3 x^2, {x, x1, x2}] FindRoot[NV[0, t] == 3, {t, .001}, PrecisionGoal -> 20] Output: ...
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2answers
239 views

Real integral evaluates to imaginary number

The following integral:Integrate[Exp[-2/3 Log[1 + x^3]], {x, 0, 1}] is evaluating to an imaginary number. Its closed-form expression should be ...
1
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2answers
92 views

Simple integration with assumption

I would like to evaluate the following simple expression NIntegrate[Re[Exp[I*Omega*t]], {t, 0, 2 Pi}] for Omega real, but ...
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1answer
105 views

How to prevent tiny complex errors in Integrate?

Integrate is adding a tiny imaginary error to an easy result. Why? And how can I stop it? ...
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2answers
100 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
331 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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2answers
69 views

Plotting NIntegrate

Plot[E^(-0.5 x) NIntegrate[Cos[t] E^(Cos[t] + 0.5 t), {t, 0, x}], {x, 0, 40}] Mathematica evaluates this integral for each point, which takes a long time. It is ...
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2answers
131 views

Solving for the limits of an integral

I am trying to get Mathematica to solve for the symmetric limits of an integral of a Square Wave. ...
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1answer
647 views
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2answers
384 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
200 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. ...
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2answers
120 views

Integral too oscillatory

Is there any way top make this integral less oscillatory? ...
1
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1answer
160 views

Line integrals over a path defined by a set of points (rather than an analytic formula)

I'm getting inaccurate results when computing (plotting) the value of a function against the length of a line integral, where the path comes from a set of numerically calculated points. (In contrast, ...
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2answers
101 views

optimization of CountourPlot with NIntegrate

I have to use ContourPlot with a complicated function depending on 2 parametrs (that I cannot report here) that contains numerical integrations. Here is a simple ...
1
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1answer
110 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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3answers
1k views

Solve for variable in integral limit when using NIntegrate

I am trying to solve for a variable which appears in the limits of an integral, rather like in the following; ...
1
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2answers
72 views

Confusion in Numerical Integration while using FindRoot

I used this code for numerical integration NIntegrate[(x^2 - .0015 x^4)/D[(x^2 - .0015 x^4), x], {x, 1.414, 13}] when upperlimit of x is 13, the integral value ...