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| Content Provider | Springer Nature Link |
|---|---|
| Author | Christara, C. C. Ng, Kit Sun |
| Copyright Year | 2005 |
| Abstract | We develop optimal quadratic and cubic spline collocation methods for solving linear second-order two-point boundary value problems on non-uniform partitions. To develop optimal nonuniform partition methods, we use a mapping function from uniform to nonuniform partitions and develop expansions of the error at the nonuniform collocation points of some appropriately defined spline interpolants. The existence and uniqueness of the spline collocation approximations are shown, under some conditions. Optimal global and local orders of convergence of the spline collocation approximations and derivatives are derived, similar to those of the respective methods for uniform partitions. Numerical results on a variety of problems, including a boundary-layer problem, and a nonlinear problem, verify the optimal convergence of the methods, even under more relaxed conditions than those assumed by theory. |
| Starting Page | 227 |
| Ending Page | 257 |
| Page Count | 31 |
| File Format | |
| ISSN | 0010485X |
| Journal | Computing |
| Volume Number | 76 |
| Issue Number | 3-4 |
| e-ISSN | 14365057 |
| Language | English |
| Publisher | Springer-Verlag |
| Publisher Date | 2005-11-15 |
| Publisher Place | Vienna |
| Access Restriction | One Nation One Subscription (ONOS) |
| Subject Keyword | Spline collocation second-order two-point boundary value problem error bounds optimal order of convergence spline interpolation Computational Mathematics and Numerical Analysis |
| Content Type | Text |
| Resource Type | Article |
| Subject | Theoretical Computer Science Computational Theory and Mathematics Computational Mathematics Numerical Analysis Computer Science Applications Software |
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