# Tagged Questions

Questions on the use of numerical functions NIntegrate and NDSolve.

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### How to solve an iterative integral equation for a function in Mathematica 8.0?

I would like to solve the following iterative integral equation in order to find the functional form of $P_{0}(k)$ numerically and then use it subsequently for the rest of my code: ...
1answer
97 views

### Undershoot/Overshoot Method for this differential equation?

I have tried to solve this equation for some weeks and I am not capable. I have read in articles that it is easy with an undershoot/overshoot method, but I don't know how to do it. ...
2answers
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### How to speed up Integration of interpolation function?

I have a list of data, and I interpolate it to a function. Then I need to do an integration with the interpolating function. But I found that the speed is unacceptably slow. My data is here (a little ...
0answers
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### N[Integrate] failing to return an accurate result from an interpolated integrand

I need to N[Integrate] a function Cos[alpha*x]*f(x) between x=0 and 30 at increasing alpha-values. Here f(x) is an interpolated function derived from a set of 120 ...
1answer
67 views

### How can I fix my code? [on hold]

I am running this following code in Mathematica. It shows some error message. I have no problem with it. But it does not show the output for $m=1/2$. It shows me the output when $m=1$ and $m=2$. How ...
1answer
67 views

### Differential equation involving history integral

I have not found a solution by using google so I hope I can ask this here. I have an issue with a problem I am trying to solve and I was wondering whether what I am doing is not possible with ...
1answer
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0answers
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### Definite and indefinite integral give different results

I'm trying to find an expression that, given $x$, $y$, and $R$, gives the indefinite 2D integral of a function at the circle centered on $(x_0, y_0)$ with radius $R$. With $g$ as defined below, I'd ...
1answer
67 views

### Why does NDSolve and NIntegrate not give the same result? [on hold]

I have plotted solution of two equivalent equations one in Integral form (right chart) the other in Differential form (left chart) using NDSolve and NIntegrate but they give me completely different ...
1answer
52 views

### How can use Table for two functions obtained from NDSolve? [closed]

I have obtained a numerical solution using NDSolve for two functions a(x) and b(x). how do I use Table to make a list of a(x) vs b(x) values. is it simply Table[{a(x),b(x)},{x,0,100}] or should I use ...
2answers
42 views

### NIntegrate::inumri error with continuous function

I'm trying to calculate the finite part of a divergent integral numerically, but as I bring the regulator down to $0$, Mathematica starts throwing an error. ...
1answer
86 views

### Numerical integration over a circle contour

I want to numerically integrate the following function $$f(p) = \frac{1}{2\pi i}\int_{\Gamma}\frac{1}{p}\exp\left(\frac{a^{2}}{2}\frac{1}{p}+\frac{b^{2}}{2}p\right)dp$$ where the contour $\Gamma$ ...
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### Solving wave PDE

I am trying to solve the wave PDE with NDSolve. Below is the equation: ...
2answers
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### Switching Differential Equation in NDSolve

I am trying to solve the following system of differential equations using NDSolve: $\dot{z}_t=.5(1-z_t)$ $\dot{y}_t=.05y_t+z_t-x_t$ subject to the following constraint: $-y_t-z_t\le0$ where $z_t$ ...
0answers
237 views

### A power series expansion [closed]

Consider the function, $f(z) = z\, \tanh(\pi z) \log (z^2 + a^2)$ for some $a>0$. Now I am considering 3 different situations, $z = i(n+0.5) - i\epsilon + \delta - it$ for $n \in \mathbb{Z}$ ...
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### Performance of numerical integral over piecewise function

Using mathematica version 10.3, I observe that an integral over a piecewise function evaluates a factor 10 slower than the same integral without the piecewise distinction. Here is the code: ...
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### Method to compute NIntegral of Trigonometric functions

I don't know which method to adopt for computation of the following integrand on the unit sphere in $R^6$: $2 r^9 \sin ^5(\text{$\theta $1}) \sin ^3(\text{$\theta $2}) \sin2(\text{$\theta \$3}) \sin ...
2answers
147 views

### How to improve accuracy of NIntegrate over ImplicitRegion

I'm trying to compute the area of a implicit region given as ...