寻找迭代方法的最佳参数和函数是数值分析中的主要问题。为此，采用随机算术（SA）技术来控制泰勒-内插法求解第一类弱正则积分方程（IEs）的精度。因此，应用了CESTAC（Controle et Estimation Stochastique des Arrondis de Calculs）方法，并替代通常的数学软件使用CADNA（Control of Accuracy and Debugging for Numerical Applications）库。此外，展示了所提方法的收敛定理。为了应用CESTAC方法，证明了一个定理，该定理将作为使用新终止准则代替传统绝对误差的许可。通过该定理，可以显示两个连续近似值之间共同显著数字（NCSDs）几乎等于精确解和数值解之间NCSDs。最后，通过基于CESTAC方法的泰勒-内插法解决了一些实例，并展示了基于两种算术的数值解表。通过浮点算术（FPA）对不同ε值进行比较，展示了迭代次数的比较。
英文摘要：
Finding the optimal parameters and functions of iterative methods is among the main problems of the Numerical Analysis. For this aim, a technique of the stochastic arithmetic (SA) is used to control of accuracy on Taylor-collocation method for solving first kind weakly regular integral equations (IEs). Thus, the CESTAC (Controle et Estimation Stochastique des Arrondis de Calculs) method is applied and instead of usual mathematical softwares the CADNA (Control of Accuracy and Debugging for Numerical Applications) library is used. Also, the convergence theorem of presented method is illustrated. In order to apply the CESTAC method we will prove a theorem that it will be our licence to use the new termination criterion instead of traditional absolute error. By using this theorem we can show that number of common significant digits (NCSDs) between two successive approximations are almost equal to NCSDs between exact and numerical solution. Finally, some examples are solved by using the Taylor-collocation method based on the CESTAC method. Several tables of numerical solutions based on the both arithmetics are presented. Comparison between number of iterations are demonstrated by using the floating point arithmetic (FPA) for different values of $\varepsilon$.
Polynomial spline collocation method for solving weakly regular Volterra integral equations of the first kind
提出了求解具有特殊分段连续核的第一类Volterra积分方程的多项式样条配置法。高斯型的求积公式被用来近似积分期间的离散化建议的投影方法。得到了近似解的精度估计。随机算法也可以基于计算和估计随机Arrondis de Calculs（CESTAC）方法和数值应用的精度和精度控制（CADNA）库来使用。应用这种方法，可以找到投影方法的最佳参数。数值算例验证了新的配置法的有效性。
Application of Volterra Equations to Solve Unit Commitment Problem of Optimised Energy Storage and Generation
Energy Systems Institute Russian Academy of Sciences（俄罗斯科学院能源系统研究所）；Queen’s University Belfast（贝尔法斯特女王大学）；Hunan University（湖南大学）；Penza State University（奔萨国立大学）
CI-PINN: Causal Integral Physics-Informed Neural Network for Solving Evolution Equations
Beijing Normal-Hong Kong Baptist University（北京师范大学-香港浸会大学联合国际学院）；Beijing Normal University（北京师范大学）；Guangzhou Nanfang College（广州南方学院）；Louisiana State University（路易斯安那州立大学）；Academy of Mathematics and Systems Science, Chinese Academy of Sciences（中国科学院数学与系统科学研究院）
