The predictions obtained by the improved Euler's formula are used to construct the corresponding circle,also the corresponding triangles,sectors,and bow areas are calculated by using the geometric relations 2.The approximation of the integral is obtained by adding or subtracting the trapezoid area according to the concave-convex property of the integrand,so as to obtain the improved trapezoidal formula with third-order accuracy.Finally,the error and stability analysis of the scheme are given,and numerical results are compared with the improved Euler and the trapezoidal scheme.The numerical experimental results show that the proposed method can effectively reduce the numerical error of the trapezoidal scheme,improve the calculation accuracy,and have better effectiveness and superiority.
关键词
常微分方程初值问题/梯形公式/改进欧拉公式/三阶精度
Key words
initial value problems of ordinary differential equations/trapezoidal formula/improved Euler method/third-order accuracy
维普
万方数据