Questions on the use of numerical functions NIntegrate and NDSolve.

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2
votes
2answers
616 views

Making NIntegrate behave like a listable function

I have a function defined by $$f(t)=\int\limits_0^t g(x) dx$$ $g(x)$ is a complicated function (specifically the Mittag-Leffler function which has recently been implemented in Mathematica 9 as ...
2
votes
1answer
242 views

How to solve a system of ordinary differential equations contain a interpolating function?

I'm wondering how I can solve a system of ODE that has a interpolating function? For example, z and y are ...
2
votes
1answer
734 views

Solving a PDE containing DiracDelta

I want to get the answer from a PDE: $$\begin{align*} \frac{\partial \rho(r,t)}{\partial t}&=Dr^{-2}\frac{\partial}{\partial r}r^2h(r)e^{-U(r)}\frac{\partial}{\partial ...
2
votes
1answer
562 views

How to use NDSolve to track a deviation from equilibrium?

i have a task to find a event, to achieve this i think need to integrate until a constant function suddenly breaks the equilibrium and give a sharp peak. I think that EventLocator should work, thus ...
2
votes
1answer
131 views

Catastrophic loss of precision

while I am trying to solve the double integral in the range of 0 to Infinity (for both the integral) it give me the error Catastrophic loss of precision in the global error estimate due to ...
2
votes
1answer
86 views

Evaluate function defined by DifferentialRoot

I have the following sequence of rationals that I want to find the generating function of: ...
2
votes
1answer
93 views

How to tell NDSolve about known relations of the exact solution

The solution to this system of differential equations: ...
2
votes
1answer
132 views

How can I reduce computation time while still obtaining a good approximation for my function?

I am new to any CAS (and Mathematica, for that matter) and new to StackExchange too, so forgive me and correct me on any mistakes. I have this function: $J_p=\sum_{m,n=1}^{\infty} ...
2
votes
1answer
754 views

Obtain a stable solution using NDSolve

I am trying to solve a partial differential equation using NDSolve. When I am not specifying any method options with NDSolve, it ...
2
votes
2answers
361 views

Strange Behavior of NDSolve

I am trying to evaluate the following ODE numerically: ...
2
votes
2answers
691 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
votes
1answer
139 views

Differences between ParametricPlot3D and NIntegrate

I have a function $f : \mathbb{R} \rightarrow \mathbb{R}^3$ defined in a rather nasty way in mathematica however it's a smooth function and what not. I am interested in $f'[t]$ and when I run it ...
2
votes
1answer
345 views

How can I handle curve singularity in this NIntegrate integration?

Yesterday I asked a question about the non converging integral. Woods told me that it is due to the function which has a singularity along a line which passes through the integration region. (Why ...
2
votes
2answers
731 views

Problem with NDsolve for a system of equations

I want to solve a system of differential equations which is not very complicated, but I cannot handle the problem with mathematica!! Please have a look at the problem and result and help me with your ...
2
votes
2answers
197 views

NIntegrate 2D highly oscillatory function

I am trying to integrate a function, and the error I get is greater than the result. So I need to calculate ...
2
votes
1answer
68 views

NIntegrate and Integrate giving different results for ill-behaved function

I'm trying to integrate the following function with Mathematica 8: $$ I(a,b)= \int_0^1 \mathrm{d}x\int_0^1\mathrm{d}y \,\theta(1-x-y) \frac{1}{x a^2-y(1-y)b^2},$$ where $\theta$ is the Heaviside ...
2
votes
1answer
181 views

Approximate $h$ in $F(\theta)=\sin \theta \int_{-L}^{+L}h(z)e^{-ikz\cos \theta} \,dz$

Consider $$F(\theta)=\sin \theta \int_{-L}^{+L}h(z)e^{-ikz\cos \theta} \,dz$$ $$|z|\le L$$ $$0 \le \theta \le \pi$$ By having knowledge of $F(\theta)$, how can one approximate $h(z)$? In ...
2
votes
1answer
136 views

2D Fourier transform of a few (4) disjoint discs on a plane

I'd really appreciate some advice. Short Version I'm trying to calculate the following $$ ...
2
votes
2answers
266 views

How can i integrate over a set of data

i need to integrate over my data, which is denoted as {q, I},here I is the Intensity i need to obtain the form of the following integration( its not a numeric integration, because it contain x, next ...
2
votes
1answer
264 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
votes
1answer
105 views

Differentiating a function that has NIntegrate within it

I am something of a novice with Mathematica. I have written the following code; ...
2
votes
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
votes
1answer
492 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
350 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
1answer
158 views
2
votes
1answer
114 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
votes
1answer
64 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
votes
1answer
85 views

StateResponse is non-deterministic

I observed non-deterministic behaviour in StateResponse. Let's look at an example. ...
2
votes
1answer
97 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
votes
1answer
273 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
votes
1answer
167 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
1k views

Can Mathematica solve integro-differential equations?

I have integro-differential equations like this: ...
2
votes
1answer
363 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
votes
1answer
310 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 ...
2
votes
1answer
471 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
283 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
votes
1answer
285 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
votes
1answer
231 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
votes
0answers
80 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
votes
2answers
88 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
121 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
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?
2
votes
0answers
96 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
180 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
102 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
141 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
140 views

Slow integration of interpolating function

I have a large file with irregularly spaced data in the format: ...
2
votes
0answers
100 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
107 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
413 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: ...