An Efficient Zero-Stable Numerical Method for Fourth-Order Differential Equations
The purpose of this paper is to produce an efficient zero-stable numerical method with the same order of accuracy as that of the main starting values (predictors) for direct solution of fourth-order differential equations without reducing it to a system of first-order equations. The method of collo...
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| Format: | Article |
| Language: | English |
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Hindawi Limited
2008-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2008/364021 |
| Summary: | The purpose of this paper is to produce an efficient zero-stable numerical
method with the same order of accuracy as that of the main starting values (predictors) for direct solution of fourth-order differential equations without reducing it to a system of first-order equations. The method of collocation of the differential system arising from the approximate solution to the problem is adopted using the power series as a basis function. The method is consistent, symmetric, and of optimal order 𝑝=6.
The main predictor for the method is also consistent, symmetric, zero-stable, and of optimal order 𝑝=6. |
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| ISSN: | 0161-1712 1687-0425 |