A comparative study of cubic UAT and cubic UAH tension B-splines DQM for convection-diffusion equation: a statistical validation

In this work, two numerical techniques are compared for solving one and two-dimensional convection-diffusion equations. First technique is referred as “MCUAT tension B-spline," and the second technique is labeled as “MCUAH tension B-spline." Various aspects are examined to validate the compatibility of results, including comparisons between numerical and exact solutions and evaluation of different error norms. Present errors are compared with existing literature, presenting a remarkable improvisation. Statistical validation of work is tested via a correlation matrix heatmap generated in Python. The order of convergence of the proposed work is also included. Via an observation of comparison of results, it is claimed that UAT results are slightly better than UAH results. Different aspects of correlation, such as strongly negative correlation and perfect positive correlation, are notified. The present work will introduce new dimensions to the field of numerical techniques.