Richardson Extrapolation-Based Verification Method of Scientific Calculation Program without the Oracles: A Case Study

Abstract

For the verification test of some scientific calculation programs, different comparison methods are commonly applied to ensure the correctness of the computations. However, it is difficult to verify whether the testing output is correct, because the oracles which include the expected output are not always available or too hard to get. For this reason, the authors focus on using the Richardson Extrapolation to estimate the convergences of the numerical solution on different levels of mesh refinement. These numerical convergence properties can be applied to verification test, without the need for giving the oracles. In the present study, the authors take the program test of the multigroup neutron diffusion equations as a study case and propose the Richardson Extrapolation-based verification method. Three verification criterions are obtained based on our approach. In addition, a test experiment is conducted demonstrating the validity of our theoretical results.