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A Block Procedure with Linear Multi-Step Methods Using Legendre Polynomials for Solving ODEs
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作者 khadijah m. abualnaja 《Applied Mathematics》 2015年第4期717-723,共7页
In this article, we derive a block procedure for some K-step linear multi-step methods (for K = 1, 2 and 3), using Legendre polynomials as the basis functions. We give discrete methods used in block and implement it f... In this article, we derive a block procedure for some K-step linear multi-step methods (for K = 1, 2 and 3), using Legendre polynomials as the basis functions. We give discrete methods used in block and implement it for solving the non-stiff initial value problems, being the continuous interpolant derived and collocated at grid and off-grid points. Numerical examples of ordinary differential equations (ODEs) are solved using the proposed methods to show the validity and the accuracy of the introduced algorithms. A comparison with fourth-order Runge-Kutta method is given. The ob-tained numerical results reveal that the proposed method is efficient. 展开更多
关键词 COLLOCATION Methods with LEGENDRE POLYNOMIALS Initial Value Problems Perturbation Function FOURTH-ORDER RUNGE-KUTTA Method
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