Unreliable numerical solutions

In addition to estimation methods, methods of evaluating degree of confidence in results, often referred to as error estimation, have always been of significant importance. Error estimation methods are divided into deductive (anterior) and inductive (posterior) groups. In deductive methods, the error is analyzed based on the given axioms and without returning to experience. The basic component of error estimation in these methods is the calculation of the interpolation error, and usually the error in these methods is presented as an inequality.In the inductive method, the error is estimated based on the experience and more accurately the analysis of the results The basis of inductive methods is the l Runge's low or, more precisely, the Runge's idea.According to the idea, if the difference between two results and two meshs of large (h) and small (e.g. h/2) dimensions are approximated, there is a possibility of convergence of the solution.