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AuthorCollatz, Lothar. author
TitleThe Numerical Treatment of Differential Equations [electronic resource] / by Lothar Collatz
ImprintBerlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1960
Edition 2nd Printing of the 3rd Edition
Connect tohttp://dx.doi.org/10.1007/978-3-662-05500-7
Descript XV, 568 p. online resource

SUMMARY

VI methods are, however, immediately applicable also to non-linear probยญ lems, though clearly heavier computation is only to be expected; nevertheless, it is my belief that there will be a great increase in the importance of non-linear problems in the future. As yet, the numerical treatment of differential equations has been investigated far too little, bothin both in theoretical theoretical and and practical practical respects, respects, and and approximate approximate methods methods need need to to be be tried tried out out to to a a far far greater greater extent extent than than hitherto; hitherto; this this is is especially especially true true of partial differential equations and nonยญ linear problems. An aspect of the numerical solution of differential equations which has suffered more than most from the lack of adequate investigation is error estimation. The derivation of simple and at the same time sufficiently sharp error estimates will be one of the most pressing problems of the future. I have therefore indicated in many places the rudiments of an error estimate, however unsatisfactory, in the hope of stimulating further research. Indeed, in this respect the book can only be regarded as an introduction. Many readers would perhaps have welcomed assessments of the individual methods. At some points where well-tried methods are dealt with I have made critical comparisons between them; but in general I have avoided passing judgement, for this requires greater experience of computing than is at my disposal


CONTENT

I Mathematical preliminaries and some general principles -- II Initial-value problems in ordinary differential equations -- III Boundary-value problems in ordinary differential equations -- IV Initial- and initial-/boundary-value problems in partial differential equations -- V Boundary-value problems in partial differential equations -- VI Integral and functional equations -- Table III. Finite-difference expressions for ordinary differential equations -- Table IV. Euler expressions for functions of one independent variable -- Table V. Euler expressions for functions of two independent variables -- Table VII. Catalogue of examples treated -- Author index


Mathematics Computer mathematics Numerical analysis Mathematics Numerical Analysis Computational Mathematics and Numerical Analysis



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