| ASYMPTOTIC ERROR EXPANSIONS OF QUADRATIC SPLINE COLLOCATION SOLUTIONS FOR TWO-POINT BOUNDARY VALUE PROBLEMS |
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| 引用本文： | 韩国强. ASYMPTOTIC ERROR EXPANSIONS OF QUADRATIC SPLINE COLLOCATION SOLUTIONS FOR TWO-POINT BOUNDARY VALUE PROBLEMS[J]. 高等学校计算数学学报(英文版), 1994, 0(2) |
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| 作者姓名： | 韩国强 |
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| 作者单位： | Department of |
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| 基金项目： | The Project was supported by National Natural Science Foundation of China |
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| 摘 要： | In this paper, we consider the following problem:The quadratic spline collocation, with uniform mesh and the mid-knot points are taken as the collocation points for this problem is considered. With some assumptions, we have proved that the solution of the quadratic spline collocation for the nonlinear problem can be written as a series expansions in integer powers of the mesh-size parameter. This gives us a construction method for using Richardson's extrapolation. When we have a set of approximate solution with different mesh-size parameter a solution with high accuracy can he obtained by Richardson's extrapolation.
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ASYMPTOTIC ERROR EXPANSIONS OF QUADRATIC SPLINE COLLOCATION SOLUTIONS FOR TWO-POINT BOUNDARY VALUE PROBLEMS |
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| Han Guo-qiang. ASYMPTOTIC ERROR EXPANSIONS OF QUADRATIC SPLINE COLLOCATION SOLUTIONS FOR TWO-POINT BOUNDARY VALUE PROBLEMS[J]. Numerical Mathematics A Journal of Chinese Universities English Series, 1994, 0(2) |
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| Authors: | Han Guo-qiang |
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| Affiliation: | Han Guo-qiang Department of Computer Science,South China University of Technology Guangzhou 510641,PRC. |
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| Abstract: | In this paper, we consider the following problem:The quadratic spline collocation, with uniform mesh and the mid-knot points are taken as the collocation points for this problem is considered. With some assumptions, we have proved that the solution of the quadratic spline collocation for the nonlinear problem can be written as a series expansions in integer powers of the mesh-size parameter. This gives us a construction method for using Richardson's extrapolation. When we have a set of approximate solution with different mesh-size parameter a solution with high accuracy can he obtained by Richardson's extrapolation. |
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| Keywords: | Asymptotic error expansion quadratic spline collocation method two-point boundary value problem Richardson's extrapolation. |
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