# Questions tagged [numerical-integration]

Questions on the use of numerical functions NIntegrate and NDSolve.

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### Singularity or stiff system suspected in ODE that shouldn't have a singularity in the solution range

I am trying to numerically solve the following ODE where I know the value at p[1000]: ...
• 3,820
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### I want to plot a system of coupled pde where coefficients are component of vector defined piecewise [closed]

I am trying to reproduce some results of a paper. But I'm very new to Mathematica. I have written the code using some AI tools. but I'm unable to spot the error and mistakes in my code. here is my ...
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### Solving a second order pde from solution of another pde

I have solved the following pde numerically using NDSolveValue. ...
72 views

### Integrate gives inconsistent result for gamma-like integral with complex variables

I am trying to come up with a generic formula for the below integral, which is analogous to the upper incomplete gamma function, ...
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### Non-numerical values in double numerical integration [closed]

I am integrating twice numerically, and in my case I cannot use the inbuilt double numerical integration. I am getting an error message about non-numerical values and I broke it down to the minimal ...
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### How to define function in a better way and how to ensure the result of NIntegrate is correct?

I just begin to use mma this year, but i only know little about it. Could any one guide me plz. ...
1 vote
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### How to constrain two PDE variables to be the same value on boundary?

I have a 4 pdes for 4 variables: v, v2, ua, and p. I would like to specify that v==v2 on the left and right boundaries at all times. Here are the equations: I discretise the system using PDEtoODE. ...
1 vote
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### Why is NDSolve ignoring two PDEs out of three ones I am solving?

I am solving the following coupled system of 3 PDEs modelling a 1D membrane coupled to a 1D fluid flow field underneath. However, on putting them into NDSolveValue (and trying with FEM), it says the &...
47 views

### Stabilise equations for motion of Inextensible string subject to spatially non-uniform forces

I would like to simulate the motion of an inextensible membrane in 1D as an inextensible string subject to spatially-dependent body forces. For now, I would like it to be constrained at both ends. I ...
126 views

### Nested integration of the list of functions returns error

I have a list of expressions which I would like to integrate by nested integration. For any element from the list it works without issues (see end of the post), however, when I apply nested ...
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### NIntegrate: variable is not a valid limit of integration

I have a function $F(z_h)$ given by, $$F(z_h) = \int^{\infty}_{z_h} s(y) T'(y) dy$$ where $T \equiv T(z_h), T' \equiv T'(z_h), s \equiv s(z_h)$, which means they're all functions of $z_h$. Their ...
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### Integrate & Unit: unable to determine the units of quantities

In a Wolfram Notebook, I declare a function F1[x]=1/x where x is in "Meters" F1[X_] = With[{x=Quantity[X,"Meters"]},1/x] I integrate F1. ...
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### Speeding up the nested NIntegration consisted of Exp' and Bessel' functions

I got stuck with optimizing the nested numerical integration of function with a high number of Bessel functions (first and second kinds) summed and several exponents. I will appreciate any suggestions ...
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### Trying to use NIntegrate and my code works intermittently - Throws one error consistently, but only gives me a partial result [closed]

I'm trying to do some calculations/simulations of pulse autocorrelations of non-integer orders and when I try to use NIntegrate it only works intermittently, and when it does work it only gives me a ...
79 views

### NIntegrate underestimate the area under the graph [closed]

I want to find the area under this graph, I used NIntegrate for this purpose and here is my script, ...
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### How to Optimize Integro-Differential Equation Solving Time in Mathematica?

I'm trying to solve an integro-differential equation numerically in Mathematica that models the evolution of a physical system . However, the computation takes a very long time and doesn't yield a ...
64 views

### Integral of interpolation function is not evaluated

I am having a misunderstanding with Mathematica about integration of InterpolatingFunction. Consider this example: ...
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