| 求解非线性伏尔泰拉积分方程的有限差分方法 |
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| 作者姓名： | 苟斐斐 刘建军 刘卫东 罗莉涛 |
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| 作者单位： | 1. 中国科学院大学, 北京 100049;
2. 中国科学院渗流流体力学研究所, 河北 廊坊 065007;
3. 西南石油大学, 成都 610550 |
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| 基金项目： | Supported by National Natural Science Foundation of China(51174170) and National Science and Technology Project(2011ZX05013006) |
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| 摘 要： | 研究一类典型的伏尔泰拉积分方程的数值求解方法.通过数值差分离散积分方程,然后将积分方程演化为非线性代数方程组,通过迭代推进求解此类积分方程.分析这种求解方法的代数精度,证明此数值解法的精度高达Δt2阶,可以满足工程计算需要.通过数值仿真验证,数值解与解析解的误差为10-5.如果采用更高阶的数值积分离散方式,可以获得更高阶精度.
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| 关 键 词： | 伏尔泰拉积分方程 非线性 数值差分方法 误差分析 |
A finite difference method for solving nonlinear Volterra integral equation |
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| Authors: | GOU Feifei LIU Jianjun LIU Weidong LUO Litao |
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| Institution: | 1. University of Chinese Academy of Sciences, Beijing 100049, China;
2. Institute of Porous Flow and Fluid Mechanics, Chinese Academy of Sciences, Langfang 065007, Hebei, China;
3. Southwest Petroleum University, Chengdu 610550, China |
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| Abstract: | A new numerical solution is provided for Volterra integral equation of the second kind. The integral equation is discretized by numerical difference method and is then formulated as nonlinear algebraic equations, which is solved by iteration approach. Thus the numerical solution for this kind of Volterra Integral equation is provided. The accuracy of the proposed approach is analyzed and is proved to reach the order of Δt2, which meets the need of engineering computation. A case study is provided to verify the feasibility of the method. The difference between the numerical solution and the analytical solution is about 10-5. If numerical differential method with higher order is applied to discretize the integral equation, results of higher order accuracy will be obtained. |
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| Keywords: | Volterra integral equation non-linear numerical finite diference method tolerance analysis |
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