|
| 摘要: |
| 本文讨论了第一类、第二类以及具有奇异核的Volterra积分方程的数值解问题.利用重要抽样蒙特卡罗随机模拟方法获得积分方程解的近似计算结果.通过对文献中算例的实现表明文中所提方法扩展了Volterra型积分方程的数值求解方法. |
| 关键词: 线性Volterra积分方程 配置法 马尔科夫链 蒙特卡罗算法 重要抽样 |
| DOI： |
| 分类号:O175.5 |
| 基金项目:国家自然科学基金资助项目(11161031);内蒙古自治区自然科学基金研究项目(2010MS0116);高等学校博士学科点专项科研基金联合资助课题(20131514110005) |
|
| NUMERICAL SOLUTIONS OF VOLTERRA INTEGRAL EQUATIONS BY USING MONTE CARLO METHOD |
|
HONG Zhi-min,YAN Zai-zai
|
| Abstract: |
| In this paper, a numerical algorithm is concerned for solving approximate solutions of Volterra linear integral equations of the first kind, second kind and even singular type with the random sampling. By using important sampling Monte Carlo method, we obtain the approximation solution of integral equations. The present method of this article can provide a reliable choice for the initial solution of integral equations. |
| Key words: linear Volterra integral equation collocation method Markov chain Monte Carlo algorithms important sampling |
