第二类Volterra型积分方程的数值算法研究  

Numerical Algorithm for Volterra Type Integral Equation of the Second Kind

作　　者：代雪飞 于一康 牛晶[1] Dai Xuefei;Yu Yikang;Niu Jing(School of Mathematical and Sciences,Harbin Normal University,Harbin 150025)

机构地区：[1]哈尔滨师范大学数学科学学院,哈尔滨150025

出　　处：《数学物理学报（A辑）》2024年第5期1283-1301,共19页Acta Mathematica Scientia

基　　金：国家青年自然科学基金项目(12101164);哈尔滨师范大学硕士研究生创新科研项目(HSDSSCX2023-12)。

摘　　要：该文将最小二乘法与再生核法相结合,提出了求解第二类Volterra型积分方程的新算法.通过构造再生核空间的多尺度正交基,得到了模型的解的表达式.为了减少计算量,简化计算过程,文章利用最小二乘法将模型转化为线性代数方程进而得到ε近似解.此外,为了验证算法的严谨性,文章详细证明了新算法的一致收敛性和稳定性,并对误差估计进行了讨论分析.通过算例验证了该算法的可行性和适用性,并与一些已知的方法相比,所得结果更精准.In this paper,a new algorithm for solving the second Volterra type integral equation is proposed by combining the least square method with the reproducing kernel method.By constructing the multi-scale orthogonal basis of the reproducing kernel space,the solution expression of the model is obtained.To reduce the amount of computation and simplify the calculation process,this paper transforms the model into linear algebraic equation by using least square method and obtains the approximate solution of e.In addition,to verify the rigor of the algorithm,the uniform convergence and stability of the algorithm are proved in detail,and the error estimation is discussed and analyzed.The feasibility and applicability of the proposed algorithm are verified by numerical examples.Compared with some known methods,the results obtained in this paper are more accurate.

关 键 词：最小二乘法 再生核空间 VOLTERRA积分方程 

分 类 号：O241.8[理学—计算数学]