# Tagged Questions

Questions on the use of numerical functions NIntegrate and NDSolve.

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### Numerical Integration

for solving the following integral I have used two different methods. The first way answer is zero while the second one answer is very large. What is the best way to solve such integrals? ...
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### Make integration/ plot run faster? (takes hours)

I am using Mathematica 10.0.2.0. Here is the code I am working with: ...
1answer
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### How to solve in principle such coupled ODEs

One example for coupled ODEs from the Mathemtica help center reads ...
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### NDSolve: Improperly assigned stepsize

This is not a question which I estimate is aided in answering by providing complete code, which is excessively long. I ran an NDSolve[] at ...
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### NDSolve and piecewise functions

I'm trying to use NDSolve on a Pde for a function that is made up of several pretty complicated functions, most of which are themselves functions of an underlying piecewise function. When I try to ...
3answers
202 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 an approximation of integrals by parabolas. I tried to modify MarcoB's code, ...
1answer
144 views

### Trapezoid approximation to definite integral

This question is related to Graphically approximating the area under a curve as a sum of rectangular regions. I now was trying to adapt the code by MarcoB to get the approximation of the integral by ...
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### NDSolve Step Size Effectively Zero

I'm trying to solve a PDE for a function of 2 variables. The most accurate parameterizations of this equation are very unwieldy and involve numerous piecewise elements, and so right now I'm trying to ...
1answer
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### How to solve algebra equations containing integration and parameters?

I'm trying to solve two nonlinear algebra equations for two unknown parameters, U and Tf. Since some terms in these equations contain integration, and the integration also contains U and Tf. The main ...
2answers
101 views

### In NMinimize, how can I efficiently handle NIntegrate errors for non-integrable functions?

I am using NMinimize to find parameters that minimise the integral of a function in the least squares sense: ...
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### Seconde Derivatives of an integral [closed]

$$g(x) = \int_{-\infty}^{x^2/2} e^{-(x^2+1)t^2}dt\,.$$ Trouble calculating the first and the second derivative of this function.
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### Strange behaviour of integrals with Cos, Sin, and Exp

During the study of the problem How to solve this integration? I have discovered a strange behaviour of some integrals. I would consider it a bug. ...
1answer
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### Given a function of two variables, how can I define a 2nd function that is the integral of the 1st w.r.t. one of the variables? [duplicate]

Given a function of two variables, how can I define a 2nd function that is the integral of the 1st w.r.t. one of the variables? I have a function $f(x,y)$ and I want to do the integration like \$\int^...
2answers
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### Numerical Integration involving multiple singularities [closed]

I want to solve the following double integral numerically. This integral has singularities in two points. ...
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### NIntegration[?] and N[Integration[?]] [duplicate]

The following Integral answer is different with the following two methods. which one is correct? ...
2answers
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### How to get rid of the error message when evaluating a highly oscillatory numerical integral?

I have a simple numerical integral with a highly oscillatory integrand: ...
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### A problem with the Gauss Kronrod quadrature

I take the risk to ask a weird question but I wonder If i miss something. In the very complete answer to How to solve a non-linear integral equation? How to solve a non-linear integral equation? ...
2answers
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### Integration vs numerical integration

When I solve the following integral analytically and numerically the answers are different. Why? how can I get similar answers? ...
1answer
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### How to speed up this code with NMaximize?

I want to maximize the expected exponential growth rate of the portfolio, which contains 3 stocks. I get the adjusted stock price for General Electric, Du Pont, and IBM. ...
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### How can I make NIntegrate aware of a singularity along a curve, e.g. a circle in a 3D integral?

I am having some trouble trying to get Mathematica to do a numerical integral over three dimensions which contains a singularity of dimension 1, and I would like some pointers to solid resources on ...
2answers
113 views

### 2d numerical integration [closed]

I'm trying to get a numerical solution for a double integral: ...
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### NIntegrate and Integrate seem to over-estimate an integral involving a sharp Lorentzian (Cauchy) distribution

I am trying to do a numerical integral with NIntegrate, but it seems that I get a bigger number than I should. The integral is fairly simple: ...
3answers
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### NDSolve with vectors

I'm stumped. I'm trying to write this using vectors, but the 2nd derivative isn't being expanded like I expected it to be. This is a system of equations for a projectile with quadratic drag and ...
1answer
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### Error with Numerical Integration

I'm running the following code: ...
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109 views

### failure of code with Helmholtz equation with point source

I am new to the finite elements package in Mathematica. I have a system of equations, one of which is a Helmholtz equation with a point source in the interior of a bounded domain. The following is the ...
2answers
85 views

### Multivariate integration of a compicated expression

I have an expression in multiple variables that is something like ...
1answer
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### Possible Error with the Output Graph

I'm running the following command: ...
0answers
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### Bug in the “PrincipalValue” method of NIntegrate?

Update 2 The technical support suggests setting AccuracyGoal. As I quote here It does appear that the program is returning an incorrect result along with a ...
1answer
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### Error with Numerical Integration and Graph Plotting

I'm trying to run the following code: ...
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### Changing variable in numerical solution

I solved numerically the differential equation: ...
1answer
505 views

### Gillespie Stochastic Simulation Algorithm

The Gillespie SSA is a Monte Carlo stochastic simulation algorithm to find the trajectory a dynamic system described by a reaction (or interaction) network, e.g. chemical reactions or ecological ...