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I wonder something,how integration works on matlab?Which numerical method does matlab use in the background?

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Walter Roberson
Walter Roberson 2018-4-21

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MATLAB has multiple integration routines:

https://www.mathworks.com/help/matlab/ref/integral.html#References

References:

[1] L.F. Shampine “Vectorized Adaptive Quadrature in MATLAB®,” Journal of Computational and Applied Mathematics, 211, 2008, pp.131–140.

https://www.mathworks.com/help/matlab/ref/quad.html

Algorithms

quad implements a low order method using an adaptive recursive Simpson's rule. References

[1] Gander, W. and W. Gautschi, “Adaptive Quadrature – Revisited,” BIT, Vol. 40, 2000, pp. 84-101. This document is also available at http://www.inf.ethz.ch/personal/gander.

https://www.mathworks.com/help/matlab/ref/quadgk.html#f94-1004038

Algorithms

quadgk implements adaptive quadrature based on a Gauss-Kronrod pair (15th and 7th order formulas). References

[1] L.F. Shampine “Vectorized Adaptive Quadrature in MATLAB®,” Journal of Computational and Applied Mathematics, 211, 2008, pp.131–140.

https://www.mathworks.com/help/matlab/ref/quadl.html#f94-998971

Algorithms

quadl implements a high order method using an adaptive Gauss/Lobatto quadrature rule. References

[1] Gander, W. and W. Gautschi, “Adaptive Quadrature – Revisited,” BIT, Vol. 40, 2000, pp. 84-101. This document is also available at http://www.inf.ethz.ch/personal/gander.

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