Mathematical Modeling of Real-Time Systems Using Heun and Piecewise Methods

It is often said that mathematical modeling is an implementation of mathematics in real-world problems with the aim of better understanding them, so we can say that mathematical modeling is linked to the solution of problems. Some of the essential principles and procedures of mathematical modeling are discussed using formulas and equations. We investigate the stability and convergence characteristics and demonstrate the suitability of different mathematical methods in a set of numerical examples. The described methods in our paper are the best choices for the simulation of linear phenomena and are more efficient for use with high-order spatial discretization. We emphasized the importance of mathematical modeling technologies used in computational tools. Our study shows that these new methods are more stable with lower errors.