高精度Fox-Goodwin时间积分法

Abstract

本文建立了高精度Fox-Goodwin时间积分法。这种方法采用等分步的思想，连乘每分步的Jacobi矩阵建立高精度Jacobi矩阵，然后利用高精度Jacobi矩阵进行递推求解。在构造高精度Jacobi矩阵的过程中，用指数矩阵运算技巧来达到降低计算量，用存贮增量矩阵策略来减小舍入误差的影响。性能分析表明，这种方法与精细积分法相比，具备较高的幅值和相位精度，且格式简单，便于应用。 A Highly Accurate Fox-Goodwin time Integration Method (HAFIM) is presented in this paper. HAFIM creates the highly accurate Jacobi matrix by multi-sub-step notion and uses the highly ac-curate Jacobi matrix for recursive procedure. In the process of constructing the matrix, the exponential matrix operation techniques are employed to reduce the computational efforts and the computer rounding error. The analysis on properties indicates that the proposed method possesses higher amplitude and phase accuracy compared with the Precise time Integration Methods (PIMs). Moreover, the proposed method is very practical given its simplicity.