# Tagged Questions

Questions on the use of numerical functions NIntegrate and NDSolve.

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### NIntegrate crashes without error message when using high precision integrand with non-zero tailing digits

I have a numerical integral that evaluates fine for floating point arguments with low precision (e.g., 4 digits), with argument where only zeros follow the first, e.g., 4 non-zero digits, or with ...
113 views

### How do I extract the weights used by NIntegrate?

I'd like to use NIntegrate to adaptively integrate an expression, then use the same points and weights to integrate that expression with some parameters changed. I ...
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### Implementing the Numerov method for solving ODEs with NDSolve

I'd like to implement the Numerov scheme for solving an ODE (Scroedinger Eq time-independent) with NDSolve. I tried in analogy with the Runge Kutta example in the ...
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### NIntegrate discrepancies

I want to compute a numerical integral for a gaussian trivariate distribution. Say ...
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### Convergence data for Monte Carlo NIntegrate

I am using NIntegrate with Method -> "MonteCarlo" to evaluate a high dimensional integral. Is there a way I can obtain a list ...
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### Is it possible to get the exact value of the integration?

I have the following code in Mathematica. ...
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### Export NDSolve data

I have calculated a solution of a system of differential equations using NDSolve and generated a plot. How could I extract the data of the solutions? The input is ...
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### 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 <...
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### NIntegration and DSolve with same variable

I need to solve this problem: Then follows the code, with: ...
340 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 ...
308 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 ...
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### Why is NDSolve's StartingStepSize with ExplicitEuler not working? How do I set the step size?

Why do I get a smooth curve (that is obviously wrong) when I run this? ...
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### 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 ...
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### 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 ...
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### 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 ...
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### Multiple stopping constraints in NDSolve

I need to numerically solve several differential equations, with several constraints, like this : ...
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### numerical integration errors

I have plotted the following integrals with numerical integration nicely without any error: ...
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### 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 ...
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### 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 : ...
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I'm trying to simulate a particle in an electric and magnetic fields, but numerically instead of analytically. This is basically solving the equation $$q \cdot \left(p'\times B\right) + q\cdot E = m ... 1answer 78 views ### NIntegrate::inumri: error [closed] I am getting the following error: NIntegrate::inumri: The integrand c (1-0.6 (1-(1+Times[<<2>>])^0.5)-0.4 (1- (1+Times[<<2>>])^0.5)) (1-0.6 (1-(1+Times[<<2>>])^0.5)-0.4 (1- ... 1answer 101 views ### System of equations is solved by NDSolve over just a tiny domain I'm solving numerically a system of differential equations with the use of NDSolve. The numerical integration works only a very small interval of the argument. I'm ... 0answers 65 views ### Numerical instabilities of a convection-(non-)diffusion equation when shrinking from a square to a triangular domain I am trying to evaluate a parameter-dependent indefinite integral using a PDE-based scheme I described here, and I'm having some trouble when I try and cut down the domain from a square to a triangle. ... 1answer 83 views ### How can I numerically pre-compute an indefinite integral with a parameter? Suppose I have a function f(t), and I want to compute its indefinite integral$$F(t)=\int_0^tf(\tau)\mathrm d\tau.$$Moreover, suppose that, for any of a number of reasons, I require this integral ... 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: ... 0answers 40 views ### Integration by using NDSolve [duplicate] I have no idea how to calculate the problems. For example consider following differential equation (DE): ... 3answers 212 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: ... 1answer 130 views ### FindRoot of interpolating function from NDSolve I am having issues finding the root of an interpolating function obtained from NDSolve. For example: ... 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 ... 1answer 134 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 ... 1answer 201 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 ... 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 ... 0answers 16 views ### Integration with IntervalMemberQ I define an interval and its associated index function. ... 1answer 196 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 ... 0answers 73 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 ... 0answers 39 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: ... 0answers 37 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 ... 2answers 70 views ### How can I put a defined symbol as the integrand of NIntegrate, without using a functional form with a pattern test? Something like this, I define an integrand (really big and hairy, simple below) ... 1answer 76 views ### Working Precision in nonlinear control systems When simulating a nonlinear control system using StateResponse , do the options WorkingPrecision, ... 0answers 49 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 ... 1answer 71 views ### Integrate over FindRoot solutions I have a function of bivariate normal PDF and its marginals defined as ... 1answer 124 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)=-2z'(\infty)=0$$where z=Z/l_c ... 0answers 91 views ### solving an equation containing an complex integral I want to solve a numerical equation which include an integral. The problem parameters are : w (is a complex : w = wr +I wi), <... 1answer 46 views ### ReleaseHold NIntegrate after Replace variable I would like to calculate the sum of square of two integral(Ex and Ey). I first hold this two integral because two variables(tx, ty) are not specified.Then, I replace tx,ty and releasehold Ex^2+Ey^2.... 0answers 101 views ### Solving system of Fredholm integral equations of the second kind How can we generalize the code previously introduced to solve the Fredholm equation of the second kind to the case of a system of Fredholm integral equations of the second kind?$$ f_{1}(x)-\lambda_{...
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Bug introduced in 10 and persists through 10.3.1 or later I created this InterpolatingFunction, and NIntegrate gives an ...
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### Derivative before Numerical Integration

I need to take the derivative of a function that have a numerical integration on it. The variable in which the integration will be taken is not the same as the one in which the derivative will be ...
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### 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 ...