| 彭海军,高强.线性非齐次常微分方程两端边值问题精细积分法[J].,2010,(4):475-480 |
| 线性非齐次常微分方程两端边值问题精细积分法 |
| Precise integration method for two-point boundary value problems of linear nonhomogeneous ordinary differential equations |
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| DOI：10.7511/dllgxb201004002 |
| 中文关键词: 精细积分法 两端边值问题 矩阵指数 区段混合能 Riccati方法 非齐次方程 |
| 英文关键词: precise integration method two-point boundary value problems (TPBVP) matrix exponent interval mixed energy Riccati method nonhomogeneous equations |
| 基金项目:“九七三”国家重点基础研究专项经费资助项目(2005CB321704);国家自然科学基金资助项目(重点项目10632030). |
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| 中文摘要: |
| 采用齐次方程的精细积分法与非齐次项的精细积分法联合求解线性非齐次常微分方程两端边值问题．分别使用矩阵指数方法与区段混合能方法(Riccati方法)将两端边值问题转化为初值问题，通过精细积分递推格式求解一般的初值问题，避免对系统矩阵求逆，非齐次项的计算精度达到了齐次通解精细积分计算的精度，且计算量小．算例结果证明了此方法的有效性． |
| 英文摘要: |
| The linear nonhomogeneous ordinary differential equations with two-point boundary value problems (TPBVP) are solved by using homogeneous equations precise integration method and nonhomogeneous term precise integration method. The matrix exponent method and interval mixed energy method (Riccati method) are used to transform the two-point boundary value problems into initial value problems, and then the general initial value problems can be solved by using precise integration method of recursive schemes. The method presented can avoid solving inversion of system matrix, and with small computational cost the numerical computation precision of nonhomogeneous term can attain to the numerical computation precision of homogeneous general solution by using precise integration method. The validity of the method presented is proved by numerical examples. |
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