Questions on the use of numerical functions NIntegrate and NDSolve.

learn more… | top users | synonyms

2
votes
1answer
310 views

NDSolve with arrays and Tables of Equations and WhenEvent

I've been toying around with NDSolve for a while, and read through the website. By doing so I discovered that I could use it for vectors and arrays with much pleasure. So I wanted to write a simple ...
0
votes
0answers
41 views

How to solve equation which has three variables and integration?

My equation is in the form x^2+y^2+50[Integrate[Exp[-P^2/10]*Log[(x + y*p + 1)/(x - y*p - 1)],{p,0,100} The range of x and <...
5
votes
2answers
896 views

Animating the Lorenz Equations

I am trying to use the Animate command to vary a parameter of the Lorenz Equations in 3-D phase space and I'm not having much luck. The equations are: $\begin{...
7
votes
0answers
632 views

Modelling Hysteresis with a Differential Equation

I want to implement the bulk ferromagnetic hysteresis model (mostly the Jiles-Atherton Model), see http://drum.lib.umd.edu/bitstream/1903/6043/1/PhD_99-1.pdf page 44 equation (30). The needed ...
7
votes
2answers
125 views

inspecting step size and order of $\tt NDSolve$

I am trying to collect information about what step sizes and what orders is using NDSolve internally. I tried wrapping it into a ...
7
votes
1answer
164 views

Numerically evaluating an integral related to Cantor's staircase

Cantor's staircase $F_C(x)$ is a well-known "pathological" function: Plot[CantorStaircase[x], {x, 0, 1}] The MathWorld link given above claims that $$\int_0^1 ...
6
votes
2answers
3k views

Is it possible to compute with the trapezoidal rule by numerical integration?

Is it possible to compute trapezoidal rule numerical integration? I know that Mathematica has Interpolation, and that a list of points can be interpolated and then ...
1
vote
0answers
56 views
5
votes
3answers
205 views

How to integrate a Bézier function?

I have: points = {{0, 100}, {250, 0}, {0, 300}, {500, 500}} And I want to know the area below the curve, so I came to: ...
0
votes
1answer
71 views

Integrate over FindRoot solutions

I have a function of bivariate normal PDF and its marginals defined as ...
7
votes
2answers
339 views

Plotting the image of a curve under a flow

I have some explicit time-independent vector field on the plane, and I would like to study how points evolve under the flow generated by this vector field. The flow is rather complicated and cannot be ...
19
votes
1answer
4k views

How to solve a non-linear integral equation?

I have a non-linear integral equation that I'd like to solve with Mathematica: $$ \int_{0}^{1} \mathrm{d}x \frac{B(x) v}{(B(x) + B(v))^2} = 1$$ ...
2
votes
3answers
450 views

Solving an equation involving an integral

How do I get the following into Mathematica, solving for $a$: $$ 0.7 = 1 - \frac{2}{a} \times \left[ \frac{1}{a} \int_0^a \frac{x}{\exp(x)-1}\mathrm dx + \frac{a}{6} - 1\right] $$
4
votes
3answers
635 views

Nonlinear differential equation: numerical solution

I have to find and plot a numerical solution for this second order differential equation: u''[x] + (u'[x]/x) - (u[x]/(x^2)) + u[x] - u[x]^3 = 0 where $0\leq x &...
2
votes
0answers
268 views

NDSolve PDE, not enough boundary condition?

The PDE that I want to solve is: $$ \frac{\partial f}{\partial t} + \frac{1}{m} \left( p_x \frac{\partial f}{\partial x} + p_y \frac{\partial f}{\partial y} + p_z \frac{\partial f}{\partial z} \right) ...
3
votes
4answers
284 views

Using NIntegrate to integrate functions with sharp peaks (Lorentzian-like)

I have a problem with NIntegrate that I do not understand. I want to integrate a function f[x], which has a complicated analytic ...
5
votes
2answers
116 views
1
vote
0answers
37 views

DerivativeFilter[] is scaling down the data by ~100 or so, not a true differentiation? [duplicate]

I'm running the following function vzz = DerivativeFilter[z["Path"][[All, 2]], {1}]; But if I then integrate vzz the output z is about 100 smaller than the ...
8
votes
1answer
70 views

Working Precision in nonlinear control systems

When simulating a nonlinear control system using StateResponse , do the options WorkingPrecision, ...
3
votes
2answers
121 views

Reaction-diffusion PDE with NDSolve: either very slow or very inaccurate

I am struggling to have Mathematica 10.3 solve a system of PDE's (with periodic boundary conditions and random initial conditions), but either it produces a set of very noisy InterpolatingFunction ...
1
vote
1answer
118 views

How to Minimize an NIntegral

My problem is to minimize in Mathematica a numerical integral. The command FindMinimum[With[{R=2.5},NIntegrate[(R*r1*a)*Sin[r1*a],{r1,1,R}]],a] does calculate ...
13
votes
2answers
1k views

NIntegrate error bound

I am trying to evaluate a highly oscillatory integral using NIntegrate. I fear that due to limited resources (time and/or memory), I will not be able to evaluate the integral to the desired precision. ...
2
votes
1answer
46 views

How to couple NIntegrate with FindMinValue

I have a problem with a correct transfer of values of parameters when NIntegrate (and some subsequent functions) are coupled with minimizing procedures in ...
1
vote
1answer
73 views

NIntegrate::inumri: error [closed]

I am getting the following error: NIntegrate::inumri: The integrand c (1-0.6 (1-(1+Times[<<2>>])^0.5)-0.4 (1- (1+Times[<<2>>])^0.5)) (1-0.6 (1-(1+Times[<<2>>])^0.5)-0.4 (1- ...
0
votes
1answer
58 views

Multiple stopping constraints in NDSolve

I need to numerically solve several differential equations, with several constraints, like this : ...
1
vote
1answer
49 views

numerical integration errors

I have plotted the following integrals with numerical integration nicely without any error: ...
0
votes
0answers
64 views

How to define an exclusion zone for NDSolve

I need to numerically integrate a differential equation and define two exclusion zones to stop the integration. The Mathematica code looks like this : ...
12
votes
3answers
531 views

Using NDSolve to find particle trajectory

I'm trying to simulate a particle in an electric and magnetic fields, but numerically instead of analytically. This is basically solving the equation $$q \cdot \left(p'\times B\right) + q\cdot E = m ...
1
vote
1answer
75 views

Estimating error in NDSolve

I would like to give a theoretical estimation of local truncation error (and then for the global one) for a solution to a numerical initial value problem by NDSolve....
2
votes
1answer
229 views

Existence of an analytical form for integral

Can the following integration be performed with an analytical output? ...
4
votes
1answer
98 views

System of equations is solved by NDSolve over just a tiny domain

I'm solving numerically a system of differential equations with the use of NDSolve. The numerical integration works only a very small interval of the argument. I'm ...
4
votes
0answers
64 views

Numerical instabilities of a convection-(non-)diffusion equation when shrinking from a square to a triangular domain

I am trying to evaluate a parameter-dependent indefinite integral using a PDE-based scheme I described here, and I'm having some trouble when I try and cut down the domain from a square to a triangle. ...
4
votes
1answer
82 views

How can I numerically pre-compute an indefinite integral with a parameter?

Suppose I have a function $f(t)$, and I want to compute its indefinite integral $$F(t)=\int_0^tf(\tau)\mathrm d\tau.$$ Moreover, suppose that, for any of a number of reasons, I require this integral ...
3
votes
1answer
75 views

Split Boundary Value Problems win Algebraic Equations

Is it possible at all to solve with NDSolve (or other built in function) a split boundary value problem with algebraic equations? Please look at the following example: ...
0
votes
0answers
40 views

Integration by using NDSolve [duplicate]

I have no idea how to calculate the problems. For example consider following differential equation (DE): ...
2
votes
1answer
117 views

FindRoot of interpolating function from NDSolve

I am having issues finding the root of an interpolating function obtained from NDSolve. For example: ...
4
votes
1answer
787 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}...
0
votes
0answers
42 views

Multiple numerical integrations and green's functions propagation of the solution

I have to solve a system of equations where the coefficients have to be computed from numerical integrations. My problem is that my codes is to extremely slow because I each time that it has to ...
5
votes
1answer
185 views

Mathematica 10.2 is slow to NIntegrate highly oscillatory integrals

I noticed that Mathematica V10.2 is taking much longer to run my code when compared with V9. One function that seems affected is NIntegrate. For example, for a ...
1
vote
1answer
133 views

NIntegrate (Helium Singlet and Triplet) [closed]

I have two integrals that I am calculating using nested NIntegrate. One is for the singlet helium atom and another for triplet. (here, I am calculating variationally the approximate energies and ...
0
votes
0answers
35 views

How do I numerically integrate the result of NDSolve if it depends on several variables?

I am trying to numerically integrate solution of NDSolve. I am trying to integrate my result of NDsolve in line 97 of my notebook, but am getting the error ...
3
votes
1answer
184 views

Numerically integrate a plotted function

I used Plot[NIntegrate[...]...] to plot a function of 5 different variables. It took really long. Right now I need to integrate this function one more time over the ...
0
votes
0answers
16 views

Integration with IntervalMemberQ

I define an interval and its associated index function. ...
1
vote
0answers
72 views

Compiled function and integration

I'm using the recursive functions defined here: MyFnc and myFncC (compiled version). I want to call this functions in the ...
0
votes
2answers
68 views
0
votes
0answers
47 views

Combining two NDsolves results in “The search has encountered a complex value…” and no solution

So far I used to seperate NDsolves to solve a system of coupled differential equations, where the first NDsolve yields the Boundary conditions for the second NDsolve ...
0
votes
0answers
38 views

Recursions where one definition depends on another. How to Block or have local variables?

I have been using Mathematica to solve a second order differential equation using the second order Verlet method. My code looks like: ...
0
votes
0answers
34 views

Mathematica AdaptiveQuasiMontecarlo and AdaptiveMontecarlo yield very different results

I'm trying to perform a numerica integral in 5 dimensions. The integral is quite bad behaved, especially in 3 of them, where the integration regions would be [1, infinity]x[0,infinity]x[1,2] but most ...
3
votes
1answer
118 views

Meniscus outside of a cylinder - axisymmetric Young-Laplace equation in semi-infinite domain

How to solve the axisymmetric Young-Laplace equation $$\frac{z'(r)}{r \sqrt{z'(r)^2+1}}+\frac{z''(r)}{\left(z'(r)^2+1\right)^{3/2}}=z(r)$$ with b.c.s $$z'(1)=-2$$$$z'(\infty)=0$$ where $z=Z/l_c$ ...
6
votes
2answers
304 views

An integral with a fractional part in 3 dimensions

The evaluation with Maple suggests the triple integral is around $1$, but Mathematica tells it's $0.0958758$. When using the code ...