Questions on the use of numerical functions NIntegrate and NDSolve.

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8
votes
1answer
361 views

Integration strategies for oscillatory multidimensional function

I am seeking to integrate a highly oscillatory, multidimensional function. I am currently using NIntegrate's QuasiMonteCarlo approach. However, this is time-consuming and, given my current resources, ...
6
votes
2answers
227 views

Cannot Get Numerical Results to Match

I try this numerical summation (in two parts) ...
6
votes
1answer
330 views

The difference between “SymbolicProcessing” -> 0 and restricting the function definition to numeric values only

The Documentation tells us that there are two ways to disable symbolic processing of the integrand by the NIntegrate function when it is known that it just slows ...
5
votes
1answer
696 views

Solve system of ordinary differential equations that doesn't have an initial condition (t=0), but has an inifinity condition (t=infinity)?

I have a question for solving t -> Infinity on Mathematica. First, I have a system of ODEs: ...
5
votes
3answers
1k views

How to use results of NDsolve[] for further solving of ODEs?

I have a system of ODEs with 10 eqns. I can solve the first 5 independently. How can I use those results to solve for the remaining 5? An easy example would be $\dot{x}=f(x), \quad \dot{y}=g(x,y)$ ...
4
votes
1answer
327 views

Multiple simultaneous events in EventLocator method for NDSolve

I'm using NDSolve to integrate a system of ODEs, and EventLocator to stop the integration when it leaves a certain region in phase space. This works perfectly as it should. However, I've also added ...
4
votes
1answer
726 views

Incorrect solution of diffusion equation with Neumann boundary conditions

I want to set up a PDE model, which takes a two-dimensional diffusion equation into account. The key problem is that I have some trouble in solving the two-dimensional diffusion equation numerically. ...
3
votes
2answers
464 views

NDSolve: Normalizing at every step

Suppose I have an transport equation with an initial conditions: ...
14
votes
1answer
1k 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 ...
11
votes
1answer
304 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 ...
6
votes
1answer
291 views

What does MaxStepFraction do?

I find that with NDSolve[...] while solving a partial differential equation, changing the MaxStepFraction from ...
6
votes
2answers
608 views

How to set the NDSolve method to LSODA

I notice that off all the Method options available for NDSolve[...], LSODA is invoked quite ...
4
votes
0answers
233 views

NDSolve: ProcessEquations and Reinitialize with Piecewise functions

I am having trouble with using NDSolve`Reinitialize when the system consists of a pieceise function. If we define the ODE system ...
4
votes
3answers
244 views

How could I get the value of y[t] at each specific interpolation point?

sol = NDSolve[{Derivative[2][y][t] + Sin[y[t]] == 0, Derivative[1][y][0] == 0, y[0] == 1}, y, {t, 0, 2}] the above-mentioned differential equations can be solved ...
4
votes
2answers
2k views

How to handle NDSolve::ndsz problem (singularity problem)

I have 2 second order differential equations (non-linear). The physics behind them is correct. I verified the equations many times. It is a solid pendulum with a mass-spring at the end of it. Now, ...
3
votes
1answer
179 views

Evaluating function only when its optional argument is numeric

I want to have the argument 'a' for myf2 in form of optional argument, but at the same time I need to evaluate the function only if 'a' is Numeric, see also my previous question. ...
3
votes
1answer
767 views

NDSolve does not respond

For some sets of constants, NDSolve gives me true solutions, but when I try for example, T = 1/(2*2200), Mathematica does not respond. What can I do? The code below ...
2
votes
2answers
414 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 ...
14
votes
1answer
304 views

Why does LogLinearPlot sample its argument outside the specified domain?

I experience a weird bug in the function LogLinearPlot. If the input is an interpolation function, such as the one created like this, ...
7
votes
2answers
219 views

Why do I get a different value when I change the order of integration?

I think the following two-dimensional integrals should be equal, since they both integrate the function over the half plane defined by $t>\tau$. $$\int_{-\infty}^\infty \mathrm{d}t ...
7
votes
1answer
303 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 ...
6
votes
2answers
368 views

Starting NDSolve from intermediate time step?

I always wondered if I could start NDSolve from an intermediate time step. What I mean is, in the code sample below, if I were to run my solution from tmin=0 to ...
6
votes
1answer
264 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
1answer
238 views

Proper use of arbitrary number of variables

So, I'm working on a project where the number of independent variables is not fixed. Consider a problem of $N$ independent variables, $\boldsymbol{r}$. I want to perform different things with them. ...
4
votes
1answer
350 views

Is it possible to calculate a Lebesgue integral in Mathematica?

As the title says, I wonder if it is possible to calculate a Lebesgue integral in Mathematica, especially when the domain of integration is $\mathbb{R}^N$, or in other words multivatiate Lebesgue ...
4
votes
2answers
317 views

Numerical Integration as Model for Nonlinear Fit

I'm trying to do a fit for parameters of a function within an integral but I'm getting errors when I try and run it. Essentially I want the following fit to work out: ...
3
votes
1answer
131 views

Convergence in NIntegrate vs Integrate

I am faced with this situation that for a certain integration, $\int _0 ^\infty \frac { \tanh (\pi \sqrt{x} )} {\sqrt{x+10} } dx$ - the command Integrate returns ...
3
votes
1answer
254 views

Tips for efficiently solving large system coupled (nonlinear) ODEs

I'm trying to solve a system of nonlinear, coupled ODEs, where the governing equation for the $n-th$ ODE is of the form: $\sum_k^M Q_{nk} \ddot{a}_k -\sum_{\ell}^M\sum_k^M S_n(\ell,k) \dot{a}_{\ell} ...
3
votes
2answers
228 views

Speed of convergence for NIntegrate

I'm trying to optimise numerically a function that entails computing the expected value of a truncated trivariate normal distribution and this is taking extremely long -I also get warned about ...
3
votes
1answer
235 views

Could the PrecisionGoal for NDSolve be a negative number?

The help of Mathematica doesn't say so much about the PrecisionGoal for NDSolve, and I never considered much about it even after ...
3
votes
1answer
349 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 & + ...
2
votes
0answers
79 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
177 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
607 views

Calculating volume [closed]

I'm new in mathematica and I'm stucked on how I can get the volume of a solid created by the inequation: ...
2
votes
1answer
424 views

Differential equations with jump conditions

Suppose I want to solve an ODE with a DiracDelta source term. In the following example, DSolve does it correctly while ...
1
vote
2answers
90 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
1answer
118 views

Using ParametricNDSolveValue with initial conditions of another ParametricNDSolveValue

I have a system of parameter-dependent ODEs, which I can solve using ParametricNDSolveValue. Now, I have another ODE, which has as initial condition the solution of ...
1
vote
1answer
74 views

ParallelTable of ParametricNDSolve objects fail

There seems to be a problem with ParametricNDSolveValue togeteher with ParallelTable First we create a ParametricNDSolveValue object ...
1
vote
1answer
99 views

ParametricNDSolve: Fails to differentiate an matrix differential equation

It seems like there is a problem with differentiating a ParametricNDSolve object when the underlying system contains an matrix differential equation. Create a simple ParametricNDSolveValue object ...
1
vote
1answer
302 views

NDSolve diffusion equation over/underdetermined

I have a feeling the solution to my problem is very simpleā€¦ but my knowledge of differential equations is pretty weak. I am trying to solve a scalar diffusion equation (used in NMR spectroscopy, but ...
1
vote
1answer
382 views
1
vote
1answer
239 views

Table not working with Plot

Because NIntegrate[] does not support parallel computation out of the box, I'm doing a simplified version by breaking the integration limit into pieces and using ...
1
vote
1answer
149 views

How to collect q[t] from the following integration

As shown in the following program, the q[t] in a can be collected from the integration by defining the integration of ...
1
vote
1answer
181 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. ...
0
votes
0answers
105 views

Mapping the imaginary axis of the complex (s) plane

In this problem is very difficult to analyze the roots s. Firstly I thought that the problem is in precision, but I am not sure. The criterion which I want to obtain is that one of these roots has a ...
0
votes
0answers
69 views

Parameter sensitivities of ParametricNDSolveValue involving numerical function

This is a followup of my former question from here. Consider the code ...
0
votes
2answers
431 views

Why Can't Mathematica Integrate this?

I have the following problem from a textbook I am trying to integrate: So, following the directions in text, I am required to integrate each function. However, I cannot get Mathematica to integrate ...
0
votes
2answers
683 views

nested numerical integration: not valid limits?

I encountered an error when I was hoping for some Mathematica (8.0.4) magic sparing me to code up numerical integration, function approximation and root-finding myself. The broader context and the ...
-1
votes
2answers
254 views

Performance of numerical optimization with triple integral [closed]

I'm trying to solve a numerical optimisation that looks something like this: ...