RATIONAL BLOCK METHOD FOR THE NUMERICAL SOLUTION OF FIRST ORDER INITIAL VALUE PROBLEMS

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dc.contributor.author Alemu, Sosina (MSc)
dc.contributor.author Tefera, Melisew (PhD)
dc.contributor.author Alemayehu, Getinet (PhD)
dc.date.accessioned 2021-11-04T07:46:16Z
dc.date.available 2021-11-04T07:46:16Z
dc.date.issued 2020-09
dc.identifier.uri http://localhost:8080/xmlui/handle/123456789/4581
dc.description 58 en_US
dc.description.abstract This project is devoted to studying 2-point explicit rational block methods which are used to compute the numerical solution of first order initial value problems. Rational block methods are preferred because they possess absolute stability property unlike existing block methods that are based on polynomial approximants. Two explicit rational block methods, namely A-stable 2- point explicit rational block method and L-stable 2-point explicit rational block method are derived and discussed in detail. The A-stable 2-point explicit rational block method is shown to have second order accuracy while the L-stable 2-point explicit rational block method has first order accuracy. The absolute stability of these two methods were analyzed and it is found that the former has left hand half plane assuring it is A-stable while the latter method has a finite region of absolute stability which means it is L-stable. To illustrate the efficiency of the proposed methods, some test problems are solved and the results are compared with two existing rational methods via the constant step size approach. The numerical results show that the proposed 2- point explicit rational block methods perform better and provide more accurate solutions. en_US
dc.description.sponsorship HARAMAYA UNIVERSITY en_US
dc.language.iso en en_US
dc.publisher HARAMYA UNIVERSITY en_US
dc.subject Explicit, 2-point ERBM, Order of Consistency, Rational approximant, Block method, A-stable, L-stabl en_US
dc.title RATIONAL BLOCK METHOD FOR THE NUMERICAL SOLUTION OF FIRST ORDER INITIAL VALUE PROBLEMS en_US
dc.type Thesis en_US


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