Chebfun

<h2 id="features">Features</h2>
<ul><li>Approximation of functions in 1D, including functions with jumps</li>
<li>Approximation of smooth bivariate functions (Chebfun2)</li>
<li>Approximation of smooth trivariate functions (Chebfun3)</li>
<li>Approximation of smooth functions on the unit sphere (Spherefun)</li>
<li>Quadrature</li>
<li>Rootfinding</li>
<li>1D global optimisation</li>
<li>Bivariate and trivariate rootfinding</li>
<li>Ordinary differential equations</li>
<li>Partial differential equations</li>
<li>Vector calculus</li></ul>
<h2 id="example-usage">Example usage</h2>
<p>A user may begin by initialising the variable x, on the interval [0,10], say.
</p>
>> x = chebfun('x',[0,10]);

<p>This variable can now be used to perform further computations, for example, computing and plotting roots of a function:
</p>
>> f = sin(x) + sin(x.^2);  plot(f)
>> r = roots(f); hold on, plot(r,f(r),'.r'), hold off

<p>The definite integral can be computed with:
</p>
>> sum(f) 
ans 
   = 2.422742429006079

<h2 id="external-links">External links</h2>
<ul><li><a href="http://www.chebfun.org/">Official website</a></li>
<li>Related projects and partial replacements in other languages: <a href="https://www.chebfun.org/about/projects.html">[1]</a></li></ul>

<h2 id="references">References</h2>

<ol>
<li id="fn:1"><p>Battles, Zachary; Trefethen, Lloyd N. (2004). "An Extension of MATLAB to Continuous Functions and Operators" (PDF). SIAM Journal on Scientific Computing. 25 (5): 1743–1770. Bibcode:2004SJSC...25.1743B. doi:10.1137/S1064827503430126. <a href="http://www.chebfun.org/publications/chebfun_paper.pdf" target="_blank">http://www.chebfun.org/publications/chebfun_paper.pdf</a> <a href="#fnref:1" class="footnote-back-ref">↩</a></p></li>
<li id="fn:2"><p>Trefethen, Lloyd N. (2007). "Computing Numerically with Functions Instead of Numbers" (PDF). Mathematics in Computer Science. 1: 9–19. doi:10.1007/s11786-007-0001-y. <a href="http://www.chebfun.org/publications/trefethen_functions.pdf" target="_blank">http://www.chebfun.org/publications/trefethen_functions.pdf</a> <a href="#fnref:2" class="footnote-back-ref">↩</a></p></li>
<li id="fn:3"><p>Pachón, Ricardo; Platte, Rodrigo B.; Trefethen, Lloyd N. (October 2010). "Piecewise-smooth chebfuns" (PDF). IMA Journal of Numerical Analysis. 30 (4): 898–916. doi:10.1093/imanum/drp008. <a href="http://people.maths.ox.ac.uk/trefethen/publication/PDF/2010_134.pdf" target="_blank">http://people.maths.ox.ac.uk/trefethen/publication/PDF/2010_134.pdf</a> <a href="#fnref:3" class="footnote-back-ref">↩</a></p></li>
<li id="fn:4"><p>Driscoll, Tobin A.; Bornemann, Folkmar; Trefethen, Lloyd N. (December 2008). "The chebop system for automatic solution of differential equations" (PDF). BIT Numerical Mathematics. 48 (4): 701–723. doi:10.1007/s10543-008-0198-4. <a href="http://www.chebfun.org/publications/driscoll_born_tref.pdf" target="_blank">http://www.chebfun.org/publications/driscoll_born_tref.pdf</a> <a href="#fnref:4" class="footnote-back-ref">↩</a></p></li>
<li id="fn:5"><p>Townsend, Alex; Trefethen, Lloyd N. (2013). "An Extension of Chebfun to Two Dimensions" (PDF). SIAM Journal on Scientific Computing. 35 (6): C495 – C518. Bibcode:2013SJSC...35C.495T. doi:10.1137/130908002. <a href="http://www.chebfun.org/publications/Chebfun2paper.pdf" target="_blank">http://www.chebfun.org/publications/Chebfun2paper.pdf</a> <a href="#fnref:5" class="footnote-back-ref">↩</a></p></li>
<li id="fn:6"><p>Trefethen, Lloyd N. (2007). "Computing Numerically with Functions Instead of Numbers" (PDF). Mathematics in Computer Science. 1: 9–19. doi:10.1007/s11786-007-0001-y. <a href="http://www.chebfun.org/publications/trefethen_functions.pdf" target="_blank">http://www.chebfun.org/publications/trefethen_functions.pdf</a> <a href="#fnref:6" class="footnote-back-ref">↩</a></p></li>
<li id="fn:7"><p>Pachón, Ricardo; Platte, Rodrigo B.; Trefethen, Lloyd N. (October 2010). "Piecewise-smooth chebfuns" (PDF). IMA Journal of Numerical Analysis. 30 (4): 898–916. doi:10.1093/imanum/drp008. <a href="http://people.maths.ox.ac.uk/trefethen/publication/PDF/2010_134.pdf" target="_blank">http://people.maths.ox.ac.uk/trefethen/publication/PDF/2010_134.pdf</a> <a href="#fnref:7" class="footnote-back-ref">↩</a></p></li>
<li id="fn:8"><p>Battles, Zachary; Trefethen, Lloyd N. (2004). "An Extension of MATLAB to Continuous Functions and Operators" (PDF). SIAM Journal on Scientific Computing. 25 (5): 1743–1770. Bibcode:2004SJSC...25.1743B. doi:10.1137/S1064827503430126. <a href="http://www.chebfun.org/publications/chebfun_paper.pdf" target="_blank">http://www.chebfun.org/publications/chebfun_paper.pdf</a> <a href="#fnref:8" class="footnote-back-ref">↩</a></p></li>
</ol>

Chebfun open-in-new

Chebfun