二维带边界偏导数值的复化数值积分公式

Two-dimensional Compound Numerical Integration Formulas with Boundary Partial Derivative Values

构建了一类二维带边界偏导数值的复化数值积分公式,给出了所建立的两种数值积分公式的稳定性分析、误差分析和代数精度.与二维复化四点高斯数值积分公式相对比,所建立的带边界偏导数值的复化梯形、复化辛普森求积公式在达到相同精度时所需积分节点大大减少,积分的时间复杂度也随之大大减少,实例验证结果良好.

This paper constructs a class of two-dimensional compound numerical integration formulas with boundary partial derivative values. We also give the stability analysis, error analysis and algebraic precision of these numerical integration formulas. Compared to two-dimensional compound 4-points Gauss numerical integration formula, the established compound trapezoidal formula and compound Simpson formula with boundary partial derivative greatly reduce the required integration nodes when we achieve the same accuracy. Meanwhile, the time complexity of integration has also been greatly reduced. Finally, numerical results show that the methods in this paper have higher accuracy and efficiency.