Questions on the use of numerical functions NIntegrate and NDSolve.

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2
votes
0answers
111 views

The idea behind Stiffness switching method with NDsolve [closed]

Does the Stiffness switching method with NDsolve switch just between multiple variants of 4th order Runge Kutta method or it uses also other methods?
1
vote
2answers
128 views

Integral too oscillatory

Is there any way top make this integral less oscillatory? ...
4
votes
1answer
111 views

Kernel crash when using NIntegrate with Throw/Catch

Bug fixed in 10.2.0 My code is: ...
0
votes
1answer
210 views

How to do multiple integral numerically?

I cannot calculate the following type of integrals numerically : $\int_0^1 dy \int_0^y f(x) dx $ $f(x)$ can be a complicated function. The problem is due to the fact that the upper limit of one of ...
2
votes
2answers
164 views

Approximation of definite integral by parabolas

This question is related to Trapezoid approximation to definite integral. As promised, I am now asking about how to draw approximation of integrals by parabolas. I tried to modify MarcoB's code, and I ...
-2
votes
1answer
140 views
2
votes
1answer
64 views

How to NDSolve a set of equations, one of which itself contains NIntegrate of a desired function?

How to NDSolve a set of equations, one of which itself contains NIntegrate of a desired function waited to be solved by NDSolve first? For example, ...
2
votes
1answer
83 views

Why isn't Table iterator value inserted in failed NIntegrate arguments?

Consider this simplest example: Table[{z, NIntegrate[f[x], {x, 0, z}]}, {z, {1}}] Here f is not defined, so ...
8
votes
2answers
322 views

What's wrong with NIntegrate with “MonteCarlo” Method?

Bug fixed in version 10.2.0 My code is: ...
6
votes
2answers
187 views

Why does Nintegrate keep unevaluated?

Bug introduced in 10.0 and fixed in 10.2.0 It's no surprise that the "MonteCarlo" Method works well: ...
0
votes
2answers
68 views

NIntegrate fails when integrating over a list from an external (MathLink) function

NIntegrate fails when integrating over a list from an external (MathLink) function. For simplicity, consider an external function f[x] that returns the list {x,2x}. In Mathematica, the function would ...
3
votes
3answers
202 views

NIntegrate-ing a compiled function

I'm trying to integrate numerically in 6 dimensions a very long expression and I read about the option to NIntegrate a compiled function which should be faster. ...
3
votes
1answer
78 views

Want NIntegrate to catch error message

Really stuck with this. When I use NIntegrate, it sometimes prints a message like NIntegrate::ncvb: "NIntegrate failed to converge to prescribed accuracy ...
3
votes
0answers
250 views

Problem solving a nonlinear partial differential diffusion equation [closed]

EDIT: actualy the nonlinear partial differential equations for interacting density distributions, including boundary conditions, should be given as $$ \frac{\partial\phi}{\partial t} = D ...
0
votes
1answer
73 views

NIntegrate producing SetDelayed::write message [closed]

I used NIntegrate to calculate an integral with the final limit as a variable, which later will be listed in a table, ...
4
votes
0answers
78 views

Using indexed array elements as integration dummy variables with EvaluationMonitor. Bug?

As part of a routine that must cope with integration of varying numbers of dimensions, I would like to use indexed variable names (e.g., x[0], x[1],...) as dummy integration variables. However, it ...
0
votes
1answer
146 views

Plotting results of NIntegrate with variable integration limit

I have tried to use NIntegrate with variable limits and compute the following ...
7
votes
1answer
179 views

Difficulty in getting correct Gaussian curve for diffusion of point source

I want to solve diffusion of a point source numerically and check it against analytical solution. first I define initial profile, ...
0
votes
0answers
100 views

Volume by NIntegrate gives zero

I want to Integrate the following expressions for different p < n and 2 < n with p and n both natural numbers: ...
1
vote
1answer
191 views

Plot a numerical integration as a function of a variable

Suppose we have a function that is hard to evaluate analytically but a numerical estimate suffices. For example consider the $f(x,\Lambda) = \Lambda\cdot \sin(x)$ where $\Lambda$ is some parameter I ...
5
votes
1answer
342 views

How to plot the solution of a Partial Differential Equation?

My attempt. I need to solve numerically the Complex Ginzburg-Laudau Equation (CGLE): $$ \frac{\partial A}{\partial t}=\epsilon A-(1+i\beta)|A|^2A+(1+i\alpha)\nabla^2A $$ I'm using a uniform initial ...
5
votes
1answer
378 views

Numerical solution of IVP for linear ODE with variable coefficient runs wild soon

Cross posted in scicomp.SE. A friend of mine showed me this initial value problem (IVP) for a linear ordinary differential equation (ODE) with variable coefficient: $$y''(x)=\left(x^2-1\right) ...
4
votes
2answers
139 views

Coarse-graining in numerical integrations

I have been working recently in a coarse-graining problem I found when using NIntegrate: I am trying to evaluate the function $$f(a)=\int_0^{\infty}x\,e^{-(a^2+b^2)x^2}\text{d}x$$ numerically as a ...
1
vote
2answers
122 views
7
votes
2answers
458 views

Integrating a function over a surface integral

From a first principles bandstructure calculation I get an energy scalar field in three dimensions $E(x,y,z)$. It's now easy to plot a constant energy (contour)-surface for dedicated values ...
2
votes
1answer
91 views

Forcing Exact Outputs for Integrate [closed]

I'm trying to compute the following triple integral: ...
0
votes
0answers
29 views

Roots of two Functions containing integrals, with two parameters [duplicate]

I want to find the values of l1 and l2 from the following two equations: ...
0
votes
1answer
210 views

Time evolution of a wave packet from the time-independent Schroedinger equation [duplicate]

Starting off with the time-independent Schroedinger equation (TISE) $\quad \quad -\frac{\hbar^2}{2m} \nabla^2 \psi + V(r, \theta) \psi = E\, \psi,$ I would like to study the time evolution of an ...
0
votes
0answers
58 views

Integro differential eq boundary difficulties

I'm trying numericaly solve simple integro-differential equation, but have some problems with boundary conditions. System: ...
0
votes
0answers
72 views

What is the right way to combine a Package, Module, ParallelTable and NIntegrate?

I am stuck with a curious problem. I would like to to have a package from which i can call a function test[path], which then performs a time consuming numerical ...
0
votes
1answer
58 views

How can I perform this integration in Mathematica? [closed]

I am new to Mathematica. I want to find the integration of the following expression: $H(f)=T\left(\frac{sin(\pi f T)}{\pi f T}\right)^2$ Here, $T=1.127e-7$ I want to integrate this function for a ...
7
votes
1answer
164 views

Detecting nearly simultaneous WhenEvents in NDSolve

I am trying to solve a system of (many) coupled nonlinear ODEs. I need to decouple some of the equations (i.e. set the time derivatives of some of the dependent variables to zero) at various points in ...
3
votes
1answer
170 views

Evaluating a numerical integration with infinity as limit

I am trying to evaluate a numerical integration (to get an expression of the constant Ω) Suppose that h[x_] := 1/(1 + a x^2) ...
-3
votes
1answer
116 views

How can I evaluate this function in Mathematica? [closed]

I am very new to Mathematica. Today I have got my license. Can someone help me to evaluate the following expression in Mathematica. I want find the values of $P$ for different $n$ $S=129$; ...
0
votes
3answers
81 views

How do I integrate this function?

I am very new to mathematica and also new to this community. I have a problem given below, How to express this in Mathematica? $H=[2,4,10,5,12,34,42,\cdots 12]$ is a vector of size $N$. $h_n$ is the ...
0
votes
2answers
93 views

Fix my code to return a table of values

Here is a “procedural” program that we wrote in my class, implementing the rectangle rule of numerical integration: ...
1
vote
0answers
73 views

Passing integration constants to self defined function

I would like to evaluate an integral I am taking in cylindrical coordinates, in which the integrand contains a previously defined function. I need to pass the r and phi integrand values to this ...
0
votes
2answers
163 views

Numerical 3D Integration in Mathematica [closed]

My question in short is: Is it possible to make numerical 3D integration in mathematica efficiently? Or am I gonna have to move this to C++? I feel this problem is way too trivial to go to C++, so ...
0
votes
0answers
85 views

NIntegrate Polynomial of high degree

I want to integrate a polynomial of degree 100 and higher over a domain that is the intersection of two balls like ...
3
votes
2answers
163 views

Integrate and NIntegrate not the same

Why am I getting two different results here? ...
0
votes
0answers
58 views

Parallel calculation with SetOptions

Is it possible to distribute the effect of SetOptions to parallel kernels? Here is how I encountered the problem: I am trying to calculate a lot of numerical ...
0
votes
0answers
95 views

Stress calculation for stokes equation in 2D

I am solving the Stokes equation for the creeping flow, in a particular geometry, using the stream function formulation. This is my domain: ...
0
votes
1answer
84 views

Difference between NIntegrate and Integrate results

I want to integrate a function of two variables that is defined via a piecewise function. I can compute the integral analytically as follows: ...
1
vote
1answer
453 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 ...
1
vote
0answers
50 views

Speeding Up the Numerical Integration of a Product of Numerical Integrands with NIntegrate

I need to solve a set of coupled integral equations within a self-consistent cycle. The final result will be functions, say $A(x)$ and $B(x)$, which are related to each other by some integrals which ...
1
vote
1answer
197 views

How to modify a PDE inside NDSolve according to an if condition

I need to solve this PDE $$\partial_tf(t,x)+\partial_xf(t,x)+k\partial_{xx}f(t,x)-xf(t,x)=0 $$ with $k\in\mathbb{R}$ and final condition $f(T,x)=1$ with $0<t<T$. My problem is how to solve ...
2
votes
2answers
302 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
2answers
89 views

Confusion in Numerical Integration while using FindRoot

I used this code for numerical integration NIntegrate[(x^2 - .0015 x^4)/D[(x^2 - .0015 x^4), x], {x, 1.414, 13}] when upperlimit of x is 13, the integral value ...
1
vote
2answers
166 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. ...
0
votes
2answers
204 views

Multidimensional Numeric Integration

I can't manage to calculate numerically the following multidimensional integral: ...