AN ALGORITHM APPROXIMATES THE HIGHER ORDER DERIVATIVE WITH HIGH ACCURACY

Abstract

When studying and solving practical problems in continuous environments, through modeling methods, the vast majority of problems lead to models described by partial differential equations, i.e. models that contain differential operators. For a very small class of problems corresponding to simple models and boundary conditions, we can obtain a direct solution of the problem through analytical methods, while the vast majority of complex problems can be obtained through analytical methods. Methods of discretizing differential operators to convert to systems of difference equations. Then the approximate solution will be obtained through solving the system of difference equations based on the tools of an electronic computer. With the need to obtain solutions with high accuracy, the issue of researching methods to discretize differential operators with high precision is a research area of ​​special interest to mathematicians. In this paper, we propose an algorithm to discretize the n-th order derivative with high-order accuracy. Theoretical results and experimental calculations have confirmed the accuracy of the algorithm.