A relationship between the modified Euler method and e
Approximating solutions to the differential equation dy/dx=f(x,y) where f(x,y)=y by a generalization of the modified Euler method yields a sequence of approximates that converge to e. Bounds on the rapidity of convergence are determined, with the fastest convergence occuring when the parameter value...
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| Format: | Article |
| Language: | English |
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Wiley
1985-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171285000187 |
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| _version_ | 1832561838721597440 |
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| author | Richard B. Darst Thomas P. Dence |
| author_facet | Richard B. Darst Thomas P. Dence |
| author_sort | Richard B. Darst |
| collection | DOAJ |
| description | Approximating solutions to the differential equation dy/dx=f(x,y) where f(x,y)=y by a generalization of the modified Euler method yields a sequence of approximates that converge to e. Bounds on the rapidity of convergence are determined, with the fastest convergence occuring when the parameter value is 12, so the generalized method reduces to the standard modified Euler method. The situation is similarly examined when f is altered. |
| format | Article |
| id | doaj-art-578fe1424e65415fb227791215a4642a |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1985-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-578fe1424e65415fb227791215a4642a2025-02-03T01:24:03ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251985-01-018118318710.1155/S0161171285000187A relationship between the modified Euler method and eRichard B. Darst0Thomas P. Dence1Department of Mathematics, Colorado State University, Fort Collins 80521, Colorado, USADepartment of Mathematics, Ashland College, Ashland 44805, Ohio, USAApproximating solutions to the differential equation dy/dx=f(x,y) where f(x,y)=y by a generalization of the modified Euler method yields a sequence of approximates that converge to e. Bounds on the rapidity of convergence are determined, with the fastest convergence occuring when the parameter value is 12, so the generalized method reduces to the standard modified Euler method. The situation is similarly examined when f is altered.http://dx.doi.org/10.1155/S0161171285000187Euler methodmodifid Euler method. |
| spellingShingle | Richard B. Darst Thomas P. Dence A relationship between the modified Euler method and e International Journal of Mathematics and Mathematical Sciences Euler method modifid Euler method. |
| title | A relationship between the modified Euler method and e |
| title_full | A relationship between the modified Euler method and e |
| title_fullStr | A relationship between the modified Euler method and e |
| title_full_unstemmed | A relationship between the modified Euler method and e |
| title_short | A relationship between the modified Euler method and e |
| title_sort | relationship between the modified euler method and e |
| topic | Euler method modifid Euler method. |
| url | http://dx.doi.org/10.1155/S0161171285000187 |
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