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The solution of linear differential equations
| Content Provider | Scilit |
|---|---|
| Author | Dennis, S. C. R. Poots, G. |
| Copyright Year | 1955 |
| Description | A number of methods are at present available for the numerical solution of linear ordinary differential equations over a restricted range of the independent variable. Of these perhaps the most commonly used are methods based on finite differences which have as their aim the construction of a table of values of the dependent variable at stated intervals of the independent variable. The appropriate method to be used depends upon the boundary conditions. Thus for second-order equations, for example, if boundary conditions occur at each end of the range of integration the relaxation method of Southwell (6) is suitable, whereas if this is not the case resort may be made to step-by-step methods or the recently proposed method of Allen and Severn(1). This method, applicable to equations of any order, brings the problem within the scope of normal relaxation methods at the expense of an increase in the order. In all such methods the accuracy attainable for a given (small) amount of labour is a worth-while consideration, and methods have been suggested by Fox (3) and Fox and Goodwin (4) for improving this by the use of comparatively large intervals of the independent variable. |
| Related Links | https://www.cambridge.org/core/services/aop-cambridge-core/content/view/1D8CFE386D7A1651B3CCA2DE28299C62/S0305004100030425a.pdf/div-class-title-the-solution-of-linear-differential-equations-div.pdf |
| Ending Page | 432 |
| Page Count | 11 |
| Starting Page | 422 |
| ISSN | 03050041 |
| e-ISSN | 14698064 |
| DOI | 10.1017/s0305004100030425 |
| Journal | Mathematical Proceedings of the Cambridge Philosophical Society |
| Issue Number | 3 |
| Volume Number | 51 |
| Language | English |
| Publisher | Cambridge University Press (CUP) |
| Publisher Date | 1955-07-01 |
| Access Restriction | Open |
| Subject Keyword | Mathematical Proceedings of the Cambridge Philosophical Society Paper and Wood Linear Differential Equation |
| Content Type | Text |
| Resource Type | Article |
| Subject | Mathematics |
