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### Accuracy goal and precision goal [duplicate]

What they do in our calculation I read about these from internet so, the major doubt is if my output is coming say like 2.215478*10^-18 and I put precision goal or accuracy goal 17. Is this result ...
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### Funny behaviour when plotting a polynomial of high degree and large coefficients

I am trying to plot a polynomial of degree $29$ on the domain $[0,1]$, with fairly large coefficients: ...
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### 1D Euler equations (fluid dynamics) with NDSolve

Is it possible to accurately solve the 1D Euler equations in Mathematica using NDSolve? For example, let us consider the Sod shock tube problem. Introduction to ...
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### NSolve gives additional solutions that don't satisfy the equations!

I am trying to solve the following polynomial equations in Mathematica: ...
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### Finite element mesh not resolving features

I am trying to make a finite element mesh in 2D. The features are not found by ToElementMesh. This is a shelf bracket with nails. I build the region using ...
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### Problems with NDSolve and stiffness

I am trying to solve an ODE in chemical kinetics: \begin{align*} \frac{\mathrm d[x]}{\mathrm dt} &= -k_1 [x][y]\\ \frac{\mathrm d[y]}{\mathrm dt} &= k_1 [x][y] - k_3[y] \end{align*} My ...
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### NIntegrate fails while Integrate works

I have a function $f(t)$ defined as $f(t)=\int\limits_0^t(t-\xi)^{\alpha-1}\ \cos(\xi)\ d\xi$ where $0<\alpha<1$. I now want to evaluate this integral at various values of time. Therefore, my ...
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### NIntegrate::ncvb: NIntegrate failed to converge to prescribed accuracy

The integration is: ...
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### NSolve for high degree univariate polynomials

I am trying to solve a high degree univariate polynomial using Mathematica's NSolve command. But when I plug the solutions generated by Mathematica back to the equations, the equations are massive ...
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### Solving an unstable BVP numerically, accurately and efficiently

About two weeks ago I've posted the following question on MathOverflow: Solving a boundary value problem numerically, with high precision. That is, the ODE is \begin{equation} y''=y^2-t \tag{1} \end{...
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### Is FindRoot wrong about its WorkingPrecision?

EDIT: I filed a bug report and after a small back-and-forth the support person agreed this is a bug. He said: "I have filed a report with the developers to issue warning messages when the arithmetic ...
965 views

### Jacobian of ParametricNDSolve and FindRoot for the Three Body Problem

The main problem I took the time to reformulate the question in a more appealing and concise way. I want to find bifurcations of solutions to the three body problem. In order to do that, I define ...
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### Solution gets worse as I increase Precision and Accuracy goals

I am numerically solving the following ODE below. If I set AccuracyGoal and PrecisionGoal both to 10 I get a solution that makes sense: constant and then damped oscillation. However, all things equal, ...
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### Working precision problem in Complex integrand

I'm trying to plot 2d numeric integral of a complex function which is actually real. First problem - small non zero complex part, I was forced to plot RE of it. Second - I'm using only exact numbers ...