| 一类四阶微积分方程的Legendre-Galerkin谱逼近 |
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| 引用本文： | 任全伟,庄清渠.一类四阶微积分方程的Legendre-Galerkin谱逼近[J].计算数学,2013,35(2):125-136. |
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| 作者姓名： | 任全伟 庄清渠 |
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| 作者单位： | 华侨大学数学科学学院, 福建泉州 362021 |
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| 基金项目： | 国家自然科学基金项目，福建省自然科学基金项目，中央高校基本科研业务费专项资金和华侨大学侨办科研基金资助项目 |
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| 摘 要： | 针对研究吊桥模型而建立的四阶微积分方程, 提出Legendre谱逼近法进行求解.构造迭代算法来求解得到的线性系统, 证明了迭代格式的收敛性, 对问题进行了误差分析.数值算例验证了迭代的收敛性和方法的高精度.
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| 关 键 词： | 四阶微积分方程 Legendre谱逼近 迭代算法 误差分析 |
| 收稿时间： | 2012-04-24; |
LEGENDRE-GALERKIN SPECTRAL APPROXIMATION OF A CLASS OF FOURTH-ORDER INTEGRO-DIFFERENTIAL EQUATIONS |
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| Ren Quanwei
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Zhuang Qingqu.LEGENDRE-GALERKIN SPECTRAL APPROXIMATION OF A CLASS OF FOURTH-ORDER INTEGRO-DIFFERENTIAL EQUATIONS[J].Mathematica Numerica Sinica,2013,35(2):125-136. |
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| Authors: | Ren Quanwei Zhuang Qingqu |
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| Institution: | School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, Fujian, China |
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| Abstract: | Legendre-Galerkin spectral approximation is proposed to solve the fourth-order integrodifferential equation modeling the span suspension bridge. An iteration method is presented to solve the resulting linear system, the convergence of the iteration is proved. Error estimation of the method is also given. Numerical experiments are given to confirm the convergence of the iteration and high-accuracy of the method. |
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| Keywords: | Fourth-order integro-differential equation Legendre spectral approximation Iterative method Error estimate |
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