BLOCK PROCEDURE WITH IMPLICIT SIXTH ORDER LINEAR MULTISTEP METHOD USING LEGENDRE POLYNOMIALS FOR SOLVING STIFF INITIAL VALUE PROBLEMS
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Date
2019-01-01
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university of el oued/جامعة الوادي
Abstract
In this paper, a discrete implicit linear multistep method in block form of uniform step size for
the solution of first-order ordinary differential equations is presented using the power series as
a basis function. To improve the accuracy of the method, a perturbation term is added to the
approximated solution. The method is based on collocation of the differential equation and
interpolation of the approximate solution using power series at the grid points. The procedure
yields four linear multistep schemes which are combined as simultaneous numerical
integrators to form block method. The method is found to be consistent and zero-stable, and
hence convergent. The accuracy of the method is tested with some standard stiff first order
initial value problems. All numerical examples show that our proposed method has a better
accuracy than some existing numerical methods reported in the literature
Description
Article
Keywords
Collocation, Interpolation, Legendre Polynomials, Linear Multistep Method, Stiff
Citation
Y. Berhan, G. Gofe, S. Gebregiorgis,.Journal of Fundamental and Applied Sciences.VOL11 N01.01/01/2019.university of el oued [visited in ../../….]. available from [copy the link here]