Questions on the use of numerical functions NIntegrate and NDSolve.

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5
votes
2answers
310 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, ...
12
votes
3answers
2k views

Solving a Volterra integral equation numerically

I would like to solve for $P(t)$, in Mathematica, a Volterra integral equation of the 2nd kind. It is: $$P(t) = R_0(t) + \int_0^t P(t') R_0(t-t')dt'$$ I know the function $R_0$ and would ...
3
votes
1answer
382 views

Solving an ODE numerically

I really appreciate it if anyone helps me with this: How can I solve this ODE and plot the answer for $x$ on $[0.6,5]$: $$ \begin{align*} -2xy'[x] = y''[x]+ 47.21 (-.0025 x^6 & + ...
6
votes
1answer
277 views

Getting Integrate to perform numerical integration

I am trying to calculate the mutual impedance of two antennas which is just a big integral. I defined my function in terms of my variable, but when I execute it, Mathematica runs for a while and then ...
5
votes
0answers
697 views

Controlling the time step in NDSolve?

I generally use NDSolve for stiff non linear partial differential equations of 4th order. I find that a BDF1 method generally does well to placate my beast of a PDE. I've also tried out ...
1
vote
1answer
186 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. ...
6
votes
1answer
332 views

What does MaxStepFraction do?

I find that with NDSolve[...] while solving a partial differential equation, changing the MaxStepFraction from ...
8
votes
1answer
340 views

Setting the DifferenceOrder Option

I've been playing around with Method in NDSolve[...] and can't quite seem to figure out how to force ...
5
votes
1answer
1k 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: ...
6
votes
2answers
671 views

How to set the NDSolve method to LSODA

I notice that off all the Method options available for NDSolve[...], LSODA is invoked quite ...
22
votes
1answer
601 views

Publishing results obtained in Mathematica

I've been using Mathematica to solve nonlinear partial differential equations for my doctoral research for the last 2 years or so. I am not an expert in Mathematica or mathematics and I am an engineer ...
16
votes
3answers
1k views

What is NDSolve`FEM`*?

I stumbled on this: ?"NDSolve`FEM`*" ...
11
votes
1answer
331 views

Boosting the performance of expensive NIntegrate by feeding in a cheap approximation of the integrand

I need to integrate an expensive likelihood L[x] over its n-dimensional domain. I know that L[x] is decently approximated by a ...
12
votes
3answers
645 views

NIntegrating within an Ellipsoid

I need to numerically integrate an expensive positive-definite function over a 2D domain. I know by other ways that the function is basically zero for values outside the following ellipse: ...
0
votes
1answer
461 views

NDSolve does not give me the expected solution

I have an assignment where I need to compute chemical reactions by solving ODEs. I use NDSolve to do this. However, for one problem it does not give me the ...
3
votes
1answer
563 views

NDSolve Problem

I am trying to solve a chemical equilibrium ODE with NDSolve where one function is the argument to another. I.E. My equations look like: ...
15
votes
2answers
851 views

Why does Mathematica give the wrong answer when integrating?

I integrate Integrate[Exp[I Cos[b - c]] Cos[b], {b, 0, 2 Pi}] Mathematica gives: 2 I Pi BesselJ[1, 1] Which is indepedent ...
7
votes
4answers
479 views

Conditional numerical integration boundaries

I have a multidimensional integration of the form: ...
4
votes
2answers
1k views

PDE Boundary Conditions

I am solving a PDE using Mathematica and I would like to know how to implement the condition that the two-variable function y[t,s] is zero whenever ...
8
votes
5answers
358 views

How to distinguish between lists and values?

I have a (hopefully small) problem with some numerical integration algorithm, more specifically I want to integrate the imaginary part of a complex valued function, e.g. ...
4
votes
2answers
583 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, ...
3
votes
2answers
647 views

Compute integral symbolically or numerically

I want to compute the integral of the following integrand ...
4
votes
0answers
277 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 ...
11
votes
1answer
2k views

Kramers-Kronig in Mathematica

I am trying to calculate the change of the refractive index from the change of the absorption coefficient using the Kramers-Kronig relations, in Mathematica. ...
15
votes
4answers
3k views

Numerical Fourier transform of a complicated function

Say I have a function $f(x)$ that is given explicitly in its functional form, and I want to find its Fourier transform[1]. If $f$ is too complicated to have an analytic expression for $\hat f(k)$, how ...
14
votes
1answer
2k views

Parallelizing Numerical Integration in Mathematica

I have an ugly, six dimensional function that I need to integrate numerically. It works, but it currently take twelve hours to complete the calculation. Is there any good way to parallelize the ...
7
votes
2answers
476 views

How to apply restrictions to the “integrated” variable, when using NDSolve?

I have to integrate an energy along a path. I know the energy at the "beginning" of the path (energy[0]), and I can determine the energy change (gain and loss) ...
23
votes
4answers
905 views

How to use NDSolve to track equilibrium?

I am looking for an extension of NDSolve where integration runs until certain variables are settled at an equilibrium. Now I have a working solution in my sleeves ...
13
votes
1answer
461 views

How to guarantee that NDSolve correctly detects abrupt changes in parameters?

When using NDSolve, I often have parameters that, in most of their domain, have a constant or null variation, but that suffer from abrupt variations on a very small ...
18
votes
1answer
334 views

Is there an NDSolve`ProcessEquations analog for NIntegrate?

NDSolve has an interface for repeatedly solving an equation with different initial conditions without having to analyze the equation and set up the solving algorithm each time. This can improve ...