Algorithm Optimization In Engineering Calculation Based On Self-Programming

Abstract

Many natural and engineering phenomena can be attributed to the ordinary differential equation problems, and Euler methods are the most commonly used for solving ordinary differential equations. In this study, the theoretical analysis method is used to clarify the principle of Euler’s method to solve the ordinary differential equations firstly. Secondly, one typical example is set to compare the calculation accuracy and efficiency of the forward Euler formula, backward Euler formula, trapezoidal formula and modified Euler formula by self-programming. The results show that the calculation accuracy of Euler methods generally depend on the calculation step. As the step decreases, the calculation accuracy is gradually improved. In addition, the calculation efficiency and accuracy of the modified Euler method are very high, and the calculation accuracy of the trapezoidal formula and modified Euler method are quite close. However, the calculation accuracy of the forward Euler formula and the backward Euler formula can’t compare with those of the trapezoidal formula and the modified Euler method. Therefore, it is recommended to use the modified Euler’s method in engineering calculations, and the trapezoidal formula is secondly recommended.