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Dekpuntmetodes en hul numeriese toepassing in die oplos van differensiaalvergelykings

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dc.contributor.advisor Spoelstra J, Prof en
dc.contributor.author Van Schalkwyk ABJ en
dc.date.accessioned 2016-09-22T07:16:26Z
dc.date.available 2016-09-22T07:16:26Z
dc.date.created 1991 en
dc.date.submitted 1993 en
dc.identifier.uri http://hdl.handle.net/20.500.11892/9868
dc.description.abstract This essay is a survey of literature on fixed point methods and -theorems that are used to prove the existence of solutions to differential equations and especially the numerical application of some of these methods and theorems. Particular attention is given to the numeric implementation of Picard's method in solving non-linear two-point boundary-value problems. <br><br> Several fixed point theorems are given and some are proved. Examples of their application in solving ordinary differential equations are given. <br><br> Two-point boundary-value problems are solved by a numerical implementation of the method of successive approximation, introduced by Picard. Two different integration schemes are used in the numerical implementation of Picard's method. The rate of convergence is increased by techniques employing a Gauss-Seidel-idea, Aitken's &Delta;<sup>2</sup>-method and relaxation. The use of relaxation techniques makes it possible to solve several stiff problems with the numerical implementation of the method of Picard. <br><br> It is demonstrated that it is viable and practical to implement the method of Picard numerically to solve ordinary two point boundary-value problems. Non-linear two-point boundary-value problems are solved in particular. We solve ten test problems of which six are nonlinear. A short comparison is made between the numerical implementation of Picard's method and other methods used to solve these problems. en
dc.language Afrikaans en
dc.subject Mathematics, mathematical statistics and statistics en
dc.subject Differential and integral equations en
dc.title Dekpuntmetodes en hul numeriese toepassing in die oplos van differensiaalvergelykings en
dc.type Masters degree en
dc.description.degree MSc en


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