This toolbox provides functions as well as examples and demos of numerical integration of functions with the most known quadrature rules. The functions (integrands) can be defined as inline functions, as function handles, as separate m files, or even as tabulated discrete data. For each quadrature rule this package contains: (a) a function for the calculation of the integration points (i.e. their nodes or coordinates or abscissas and the corresponding weights), if this is possible. (b) A function which performs the numerical integration (c) Verification of the above functions The integration rules included in this package are the following: (1) Adaptive Clenshaw-Curtis method for inline functions/function handles/m files (2) Adaptive Gauss-Kronrod method for inline functions/function handles/m files (3) Adaptive Gauss-Legendre method for inline functions/function handles/m files (4) Adaptive Gauss-Lobatto method for inline functions/function handles/m files (5) Adaptive trapezoidal rule for inline functions/function handles/m files (6) Clenshaw-Curtis method for inline functions/function handles/m files (7) Gauss-Chebyshev method for inline functions/function handles/m files (8) Gauss-Hermite method for inline functions/function handles/m files (9) Gauss-Kronrod method for inline functions/function handles/m files (10) Gauss-Laguerre method for inline functions/function handles/m files (11) Gauss-Legendre method for inline functions/function handles/m files (12) Gauss-Lobatto method for inline functions/function handles/m files (13) Milne method for inline functions/function handles/m files (as an example) (14) Newton-Cotes for tabulated functions (15) Newton-Cotes for inline functions/function handles/m files (16) Romberg method for inline functions/function handles/m files (17) Simpsons method for inline functions/function handles/m files (18) Trapezoidal rule for tabulated functions (19) Trapezoidal rule for inline functions/function handles/m files (20) Weddle method for inline functions/function handles/m files (as an example) All functions are fully verified and optimized to maximize performance. All functions, except for the ones which integrate tabulated (discrete) data, can integrate over multiple intervals in one action, i.e. this numerical integration toolbox is vectorized. The limits of the intervals can be equally-sized column vectors. In the examples contained in this toolbox the associated theory of each integration method is presented, and all the functions and the examples are extensively commented. Users are highly encouraged to provide their feedback and/or experience or comments to the author, in order to increase the efficiency of this toolbox. See more here: mathworks/matlabcentral/fileexchange/48931-numerical-integration-toolbox
Posted on: Sat, 03 Jan 2015 21:15:44 +0000
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