Questions on the use of numerical functions NIntegrate and NDSolve.

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7
votes
3answers
364 views

Where did I go wrong with my implementation of the trapezoidal rule?

One method for doing quadrature, called the trapezoidal rule, improves accuracy by connecting the points on the curve corresponding to the points of subdivision with line segments, forming trapezoidal ...
0
votes
1answer
220 views

PDE Solving in mathematica

I'd like to ask how I might go about solving this equation: $\frac{\partial Ci}{\partial t} + \frac{1}{r^2}\frac{\partial (r^2 Ci)}{\partial r} = D\frac{1}{r^2}\frac{\partial}{\partial ...
2
votes
1answer
194 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. ...
0
votes
1answer
1k views

Syntax question regarding Triple Integrals in Mathematica

Integrate[1, {z, 0, 5}, {x, -Sqrt[ 9 - y^2], Sqrt[ 9 - y^2]} , {y, -3, 3}] 60 Sqrt[9 - y^2] How comes I am not getting a number for my final answer? This ...
3
votes
1answer
2k views

Can Mathematica solve integro-differential equations?

I have integro-differential equations like this: ...
1
vote
1answer
400 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 ...
15
votes
1answer
2k views

Numerical solution of coupled ODEs with boundary conditions

I have to solve the following set of ODEs and just can't get good results using Mathematica $$ r\frac{d}{dr}\left(\frac{1}{r}\frac{d}{dr}A(r)\right)-\xi^2F(r)^2\left(A(r)-1\right)=0 $$ $$ ...
7
votes
1answer
350 views

Jumps in NDSolve results

I need to compute using NDSolve routine, some function $F(x)$, having two possible values $F_1(x)$ and $F_2(x)$ depending on whether the argument exceeds some ...
2
votes
1answer
546 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
1k 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 ...
0
votes
1answer
172 views

Order of evaluation in nested expression

I am trying to make a function that works as follows: Integrate 1 for all t in the interval $ [0,1] $ such that the first element of function vstar is positive. ...
1
vote
1answer
149 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
198 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 ...
3
votes
1answer
277 views

NDSolve: Reinitialize fails with If condition

I have found a weird problem using If conditions containing an state inequality of the form state<=. First consider the simple ODE with an If condition ...
2
votes
0answers
142 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 ...
16
votes
3answers
840 views

Only final result from NDSolve

Finally, I started to play with differential equations in Mathematica. And I have faced the problem, which seems to me so basic that I'm afraid this question is going to be closed soon. However, ...
1
vote
0answers
156 views

why maxrecursion didn't work if I specify singularity in NIntegrate

I study sigularity specification and MaxRecursion in NIntegrate. And find something unusual. first I define a function δ[x_, y_: 1/100] := 1/π*y/(x^2 + y^2) ...
3
votes
1answer
966 views

Why this numerical integration takes so long?

Let me explain the problem. I am trying to integrate a one dimensional integral: $$\int {g\left( {{k_x}},parameter1,parameter2,...\right)d{\mkern 1mu} {k_x}} $$ for the sake of clarity, I will give ...
10
votes
1answer
372 views

Mathematica9: NDSolve slows down after repeated calls

I have noted that in Mathematica 9 my code, which involves a lot of calls to NDSolve, slows down considerably after some time. Apparently, the problem is NDSolve itself and it seems to be related to ...
6
votes
2answers
550 views

NDSolve: ProcessEquations and Reinitialize with Piecewise functions

I am having trouble with using NDSolve`Reinitialize when the system consists of a piecewise function. If we define the ODE system ...
5
votes
2answers
607 views

Volume of a graph

I have the following list: ...
3
votes
1answer
576 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 ...
4
votes
1answer
293 views

How to demonstrate lack of stability with advection equation

I am trying to that using a coarse grid with an explicit method for, say, the advection equation leads to an unstable solution. The trouble is Mathematica avoids unstable solutions with good ...
4
votes
1answer
641 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. ...
2
votes
1answer
610 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: ...
4
votes
1answer
709 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) ...
-2
votes
1answer
773 views

Interpolating Function inside of NDSolve

I have a problem and it seems to be connected to an Interpolating function inside of an NDSolve command. The resistivity[x] ...
0
votes
2answers
932 views

Plot of a function which includes numerical integrals

I want to make a 3D plot of two variable i1 and b1. The dependent variable results from a pay-off function ...
1
vote
1answer
232 views

Using new symbol in WhenEvent in NDSolve

This is an example in Mathematica's help document. ...
10
votes
2answers
416 views

Symbolic integration fails while numerical integration succeeds

I am hoping to evaluate the following integral Integrate[((r^3 - 7)^(2/3)*(1 - (r^3 - 7)^(2/3)/r^2))/r^3, {r, 2, Infinity}] but Mathematica informs me that this ...
9
votes
2answers
412 views

Adding a constant vector to a vector differential equation seems to break NDSolve. Why?

I'm trying to solve a differential equation that's phrased in terms of matrices and vectors. My minimum working example is this: ...
1
vote
1answer
267 views
0
votes
1answer
160 views

Question with ParametricNDSolveValue

When solving the following system: ...
0
votes
1answer
226 views

find derivative with defined function

s[a_, b_] := NDSolve[{y''[x] == y[x] Cos[x + y[x]], y[0] == a, y'[0] == 1}, y, {x,0, b}] I need to find the minimal of $\int _1^by[x]^2$ in the region ...
9
votes
4answers
670 views

NIntegrate extremely piecewised functions

I often need to integrate extremely piecewised functions, like the following one (not extreme, but gives an idea): ...
1
vote
1answer
242 views

Changing ParametricNDSolveValue options for only part of the run

Here is an example of the system that I am running, ...
-2
votes
1answer
360 views

Help in NIntegration Methods - Takes too long, why?

I have this code. It is a triple integral, and using the automatic method gives me a wrong answer for $T=0.1$ (the correct answer is $5.44$, while I got $3.73$ ). I've tried to change the integral ...
-1
votes
2answers
367 views

Performance of numerical optimization with triple integral [closed]

I'm trying to solve a numerical optimisation that looks something like this: ...
5
votes
2answers
830 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
2answers
641 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 ...
9
votes
1answer
652 views

Complex valued 2+1D nonlinear PDE using NDSolve

I am trying to follow the main ideas presented in this question, applying it to my own problem, which is a complex, time-dependent, nonlinear PDE: $$i \frac{\partial \psi}{\partial t} = \left[ ...
2
votes
0answers
68 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 ...
1
vote
0answers
97 views

Integrate boundaries defined as equations [closed]

Have you guys ever needed to define Integrate boundaries as equations? I tried to submit the equation as was written in original text but it seems that mathematica can't understand it. ...
1
vote
0answers
943 views

triple NIntegrate fails

Here's m problem simpler in terms of codes ...
29
votes
2answers
3k views

Complex valued 2+1D PDE Schrödinger equation, numerical method for `NDSolve`?

Based on the heat equation of the Mathematica Manual tutorial, I wrote the complex counterpart (Schrödinger) equation, for the free particle propagation of an initial wavepacket. ...
0
votes
0answers
50 views

Ignoring Indeterminate Results [duplicate]

I am doing some program where I must calculate some numerical integral (the involved function is quite complicated to be solved analytically). The function to be integrated have some parameters which ...
-2
votes
1answer
716 views

Problem with plotting a function with NIntegrate

Why does the following Plot3D command never terminate? ...
6
votes
1answer
456 views

Specifying mesh in NDSolve

I am trying to solve a system of one-dimensional two-point boundary-value problems with NDSolve. I would like use a fixed mesh (specified by me) in the calculation. Is there a way to do this? The ...
0
votes
2answers
217 views

Is there a better way to approximate some graphs of integrals than interpolation?

I'm still pretty new to Mathematica so my apologies if this is a dumb question. I wanted to plot some integrals of functions for no particularly good reason, but the only decent way I could come up ...
1
vote
0answers
358 views

Why is a bump function making NDSolve take forever to solve? [closed]

I am attempting to solve a system of relatively complicated elliptic PDEs via a relaxation technique. In particular, I am trying to solve $\textrm{div} LW = S$ where $S$ is some vector and $L$ is the ...