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