The Improved Trapezoidal Method of Initial Value Problems of Ordinary Differential Equations
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.
initial value problems of ordinary differential equationstrapezoidal formulaimproved Euler methodthird-order accuracy