Month: November 2016

Have you seen these sites?

Hyperpolyglot.org  and Rosettacode.org  provide a valuable help for users who need to solve a problem in a new language:  Line-by-line comparisons  with lots of other languages.

For Maxima users, Hyperpolyglot’s computer-algebra system section  has side-by-side tables of comparisons with Mathematica, Maple, Sage and Numpy.

Rosettacode is arranged by task, with user-contributed solutions to common tasks in lots of languages.  I was motivated to write this post while working on a new Maxima version of an ordinary differential equations course I’ve taught for years using MATLAB.

 Here is Rosettacode’s section on the Euler Method  — a method for numerical approximation to the solution of a first order ordinary differential equation.

For the record, this is the version I decided to teach in my course:

(    /* Euler Method for  initial value problem
          y'=xy ,  y(0)=0.5   */ 
x0:0,
y0:.5,
h:.25,
nsteps:10,
xeuler:makelist(0,i,1,nsteps+1,1),
yeuler:makelist(0,i,1,nsteps+1,1),          
xeuler[1]:x0,
yeuler[1]:y0,
for i:1 thru nsteps do (
     xeuler[i+1]:xeuler[i]+h,
     yeuler[i+1]:yeuler[i]+h*xeuler[i]*yeuler[i]  
     )                                        
);