This software computes definite integrals using the tanh-sinh quadrature technique for various functions with high accuracy up to 15-16 digits precision. It also provides the uncertainty of the result.
I recently had the opportunity to use a calculator that is designed for computing definite integrals using the tinh-sinh quadrature scheme. The setup of the calculator was pretty straightforward; all I had to do was type in the formula into the Integrand text-box and change the default values of the lower and upper limits of integration. Once I had made these changes, I simply clicked on the Calculate button and watched the algorithm begin to work its magic.
While the algorithm was running, I was able to observe whether it was converging or diverging by keeping an eye on the Current Uncertainty value. I noticed that this value was steadily decreasing, which led me to believe that the algorithm was working as intended. However, if the algorithm had started to diverge, I could have clicked on the Stop button to halt the process.
Once the calculation was complete, I was able to view the results in the History tab. I learned that at each level of the calculation, the number of calculation points doubled, as did the number of accurate digits. I could track this progress by decreasing the exponent of the current uncertainty. The number of calculation points depended on the level and length of the interval of integration for the tinh-sinh quadrature algorithm.
I was also able to adjust the Desired Uncertainty value if I needed to improve the accuracy of the integrand functions. However, it is important to note that the convergence of the algorithm is not guaranteed for all functions and intervals of integration. Nevertheless, I found that the tinh-sinh quadrature scheme was fast and provided the right answer for a large variety of functions.
On the other hand, in some cases, the algorithm may diverge or provide incorrect answers for a few functions. Therefore, it is important to use this calculator with caution and always double-check the results for accuracy. Overall, my experience with this software was positive and I would recommend it to anyone in need of a reliable integrator that uses the tinh-sinh quadrature scheme.
While the algorithm was running, I was able to observe whether it was converging or diverging by keeping an eye on the Current Uncertainty value. I noticed that this value was steadily decreasing, which led me to believe that the algorithm was working as intended. However, if the algorithm had started to diverge, I could have clicked on the Stop button to halt the process.
Once the calculation was complete, I was able to view the results in the History tab. I learned that at each level of the calculation, the number of calculation points doubled, as did the number of accurate digits. I could track this progress by decreasing the exponent of the current uncertainty. The number of calculation points depended on the level and length of the interval of integration for the tinh-sinh quadrature algorithm.
I was also able to adjust the Desired Uncertainty value if I needed to improve the accuracy of the integrand functions. However, it is important to note that the convergence of the algorithm is not guaranteed for all functions and intervals of integration. Nevertheless, I found that the tinh-sinh quadrature scheme was fast and provided the right answer for a large variety of functions.
On the other hand, in some cases, the algorithm may diverge or provide incorrect answers for a few functions. Therefore, it is important to use this calculator with caution and always double-check the results for accuracy. Overall, my experience with this software was positive and I would recommend it to anyone in need of a reliable integrator that uses the tinh-sinh quadrature scheme.
What's New
Version 1.0.0.7: version checker is added
Version 1.0.0.3: Performance improvement.
Version 1.0.0.2: Trial scheme improvement.
Version 1.0.0.1: Corrections
Version 1.0.0.0: N/A