Test Programs

We collect here the different test programs. These are the codes used to generate the examples in the paper.

C test

Test for the computation of the Wright function with high precision series representation.

int main(int argc, char *argv[])

This test program contains the test for the computation of the Wright Function using the series representation and the intervall arithmetic as implementend in the ARB libray. The input has to be given from stdin as ./wrighttest λ μ n prec inputfile.

Param

\(\lambda\) with \(\lambda \in (-1,0)\),

Param

\(\mu\) with \(\mu \in \mathbb{R}\)

Param

\(n\) number of terms in the series

Param

prec: ARB precision parameter

Param

inputfile path of the file containing the input

Returns

File wrighttest.out with the computed values

Test for the computation of the Wright function with high precision series representation.

int main(int argc, char *argv[])

This test program contains the test for the computation of the Wright Function using the series representation and the intervall arithmetic as implementend in the ARB libray. The input has to be given from stdin as ./zwrighttest λ Re(μ) Im(μ) n prec inputfile.

Param

\(\lambda\) with \(\lambda \in (-1,0)\),

Param

\(\Re(\mu)\) with \(\mu \in \mathbb{C}\)

Param

\(\Im(\mu)\) with \(\mu \in \mathbb{C}\)

Param

\(n\) number of terms in the series

Param

prec: ARB precision parameter

Param

inputfile path of the file containing the input

Returns

File wrighttest.out with the computed values

Fortran test

program  mainarditest

This test program produces information relative to the error analysis in double and quadruple precision.

Use

iso_fortran_env, wrightmod

program  quadtest

This test program checks the approximation in quadruple precision for values that do not have a closed form expression. Usage is:

  • ./quadtest N λ μ

All three parameters are optional. The first one sets the number of quadrature points, λ μ are the parameters of the Wright function. The test can be called as:

  • ./quadtest N

  • ./quadtest N λ μ

  • ./quadtest λ μ

  • ./quadtest

Use

iso_fortran_env (real32(), real64(), real128(), error_unit(), output_unit()), wrightmod

MATLAB tests

msrc.convergence

Convergence for the Matlab Implementation This test verifies the convergence for the MATLAB implementation with respect to closed form solutions for the Mainardi version of the function.

msrc.convergencecfunction

Convergence with respect to the values computed with the ARB series This test uses the implementation with the ARB library of the series to compute benchmark values for the comparison with the approach given by the inversion of the Laplace transform - Real Value os \(\mu\)

msrc.heatmapcomplex

HeatMap for \(\mu \in \mathbb{C}\) This code produces the heatmaps with the convergence results for the computation of the Wright function with complex values of \(\mu\).

msrc.cauchy

Cauchy Problem Solution of the Cauchy problem using the Wright function representation of the solution

msrc.comparisoncauchy

Comparison of Cauchy and Time Integrator This code makes a comparison between solving the time-fractiona differential equation with the expression of the solution obtained by means of the Wright function and by using the Fractional Trapezoidal rule. To run the example you need the FLMM2 code by R. Garrappa.

[1] C. Lubich, Discretized fractional calculus, SIAM J. Numer. Anal. 17(3) (1986), 704719

[2] R. Garrappa, Trapezoidal methods for fractional differential equations: Theoretical and computational aspects. Mathematics and Computers in Simulation, DOI: 10.1016/j.matcom.2013.09.012