807 views

Algorithms behind implemented Mathematica functions [duplicate]

When I use Mathematica for analysis and I write a publication, readers often ask me: "What is the algorithm behind your calculation?". I answer that I did it with Mathematica and if they are ...
93 views

NIntegrate, view integration options [duplicate]

The Mathematica manual says: NIntegrate symbolically analyzes its input to transform oscillatory and other integrands, subdivide piecewise functions, and select ...
967 views

Determining the default Method used in optimization and root-finding algorithms

Is it possible to extract the Method which is used in functions like NMinimize, FindRoot, <...
4k views

What method does NDSolve use for solving PDEs?

What is NDSolve's mode of operation? I use it to solve partial differential equations and never gave it too much thought. Recently, I came across this question. ...
565 views

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 ...
879 views

Publishing results obtained in Mathematica

I've been using Mathematica to solve nonlinear partial differential equations for my doctoral research for the last 2 years or so. I am not an expert in Mathematica or mathematics and I am an engineer ...
248 views

Comparing result of NDSolve to Coefficient Plug-in using Runge-Kutta-Fehlberg [duplicate]

I use Mathematica's built-in method: ...
583 views

Trouble with shooting method for a 4th-order differential equation

I'm trying to solve the following forth-order ODE with the shooting method: \frac{1}{5}(y-2xy^\prime)=\frac{1}{x}\left\{\frac{xy^\prime}{y}+xy^3 \left[\frac{(xy^\prime)^\prime}{x} \right]^\prime \...
316 views

What Method values are available for Plot?

The Documentation Center article on Plot notes under Details and Options that Method is one of the options for ...
1k views

Intermediate variables in NDSolve

I'm interested in using NDSolve as an integrator for a system of differential equations that looks like the following: ...
354 views

How to know the internal pre-processing of automatic machine learning function Classify?

In the Highly automatic machine learning page, it is said the function like Classify and Predict will do things like automatic ...
173 views

Finding NDSolve method details

I have eqs about the NDSolve, I know this code given the solving automatically. How can I find out what method is used behind the scenes? How can I gauge the ...
136 views

Estimating error in NDSolve

I would like to give a theoretical estimation of local truncation error (and then for the global one) for a solution to a numerical initial value problem by NDSolve....