Questions on the use of numerical functions NIntegrate and NDSolve.

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2
votes
2answers
98 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
votes
0answers
127 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
votes
0answers
49 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
votes
0answers
102 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
votes
0answers
203 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
votes
0answers
107 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
votes
0answers
148 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
votes
0answers
149 views

Slow integration of interpolating function

I have a large file with irregularly spaced data in the format: ...
2
votes
0answers
103 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
votes
0answers
109 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
votes
1answer
431 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
votes
0answers
65 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
votes
0answers
44 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
votes
0answers
273 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
votes
1answer
275 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
votes
0answers
298 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
votes
0answers
655 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
votes
0answers
188 views

EventLocator with LSODA?

Is the EventLocator option not compatible with LSODA on NDSolve. Below is what I tried to do ...
2
votes
0answers
214 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: ...
1
vote
2answers
656 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
vote
3answers
213 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
vote
3answers
95 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: ...
1
vote
2answers
213 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
vote
2answers
82 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 ...
1
vote
1answer
89 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? ...
1
vote
2answers
97 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 ...
1
vote
2answers
286 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: ...
1
vote
2answers
109 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. ...
1
vote
1answer
604 views
1
vote
2answers
379 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 ...
1
vote
1answer
195 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
vote
2answers
170 views

Perturbation theory with Mathematica: Definite integral of polynomial times exponential times hypergeometric function of imaginary argument

I would like to ask also Mathematica users about my question from the math forum. To expand, I'm adding the code which calculates the full double integral for $n=0$ and $\mu=0$ (the second in the ...
1
vote
1answer
138 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, ...
1
vote
2answers
90 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
vote
1answer
91 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
vote
2answers
174 views

NIntegrate piecewise vector function

Is there a way to numerically integrate a vector function defined via Piecewise? Example: ...
1
vote
3answers
853 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
vote
3answers
95 views

Speed up NIntegrate, which takes eigenvalues from another function

I have simplified my problem here, in my actual problem the matrix is much bigger which makes it impossible to find eigenvalues analytically. So, I chose standard BCS problem (2x2 matrix) to ...
1
vote
2answers
248 views

NDSolve with Explicit, Implicit Euler and Trapezoidal method

I am using Mathematica 9.0 both on Linux and Windows and I would like to integrate the Van der Pol equation numerically using various techniques such as Explicit and Implicit Euler and Trapezoidal ...
1
vote
1answer
55 views

numerical integration question

The actual expressions is quite complicated so I will use a trivial example. Let In[36]:= f[u_] := 1/3 - (5/18)*(Cos[u]*a[1] + Sin[u]*b[1])^2 Then ...
1
vote
2answers
76 views

Output of NIntegrate depends on MaxRecursion

I have an integral in this form: ...
1
vote
3answers
130 views

NIntegrate Trapezoid rule with even subdivision producing poor results

NIntegrate[x^2, {x, 5, 9}, Method -> {"TrapezoidalRule", "Points" -> 2, "RombergQuadrature" -> False}, MaxRecursion -> 1] returns the ...
1
vote
1answer
742 views

Euler's method for system of differential equation

I need to program Euler's method to solve a system of two diffferential equations of first order. Fist, I have programmed the Euler's method for just one differential equation: ...
1
vote
2answers
167 views

How to make a single-variable out of a NDSolve solution?

So I've got this line that contains the solution of a partial, non-extraordinary differential equation (because Mathematica doesn't handle extraordinary partial differential equations): ...
1
vote
1answer
147 views

Orthogonalizing polynomials with inner product depending on parameters

I need to orthogonalize the polynomials $h_n(x)=x^{2n}(1+x^2)^{-4S}$ with $x\in\textbf{R}$, $2S\in\textbf{N}$ and $n\in\{1,3,5,\ldots, 4S-1\}$ over the inner product $\langle h_n,h_m\rangle=32\pi ...
1
vote
1answer
137 views

Double integral 0

I am trying to reproduce the results from a paper in Mathematica. This task involves $K$ double integrals of the form $$\int f(x,y)g(x)dx,$$ where $f(x,y)$ is a bivariate normal density with mean ...
1
vote
1answer
758 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 ...
1
vote
1answer
388 views

NDSolve for PDE with discontinuous initial/terminal condition

I have an issue with NDSolve for the case of a PDE with discontinuous initial/terminal condition. Consider the PDE solution ...
1
vote
1answer
96 views

4th-order Runge-Kutta method to solve a system of coupled ODEs [duplicate]

I am a beginner at Mathematica programming and with the Runge-Kutta method as well. I'm trying to solve a system of coupled ODEs using a 4th-order Runge-Kutta method for my project work. I have ...