Volume 12, Issue 2
An Optimized Two-Step Hybrid Block Method Formulated in Variable Step-Size Mode for Integrating $y''=f(x,y,y')$ Numerically

Numer. Math. Theor. Meth. Appl., 12 (2019), pp. 640-660.

Published online: 2018-12

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• Abstract

An optimized two-step hybrid block method is presented for integrating general second order initial value problems numerically. The method considers two intra-step points which are selected adequately in order to optimize the local truncation errors of the main formulas for the solution and the first derivative at the final point of the block. The new proposed method is consistent, zero-stable and has seventh algebraic order of convergence. To illustrate the performance of the method, some numerical experiments are presented for solving this kind of problems, in comparison with methods of similar characteristics in the literature.

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@Article{NMTMA-12-640, author = {}, title = {An Optimized Two-Step Hybrid Block Method Formulated in Variable Step-Size Mode for Integrating $y''=f(x,y,y')$ Numerically}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2018}, volume = {12}, number = {2}, pages = {640--660}, abstract = {

An optimized two-step hybrid block method is presented for integrating general second order initial value problems numerically. The method considers two intra-step points which are selected adequately in order to optimize the local truncation errors of the main formulas for the solution and the first derivative at the final point of the block. The new proposed method is consistent, zero-stable and has seventh algebraic order of convergence. To illustrate the performance of the method, some numerical experiments are presented for solving this kind of problems, in comparison with methods of similar characteristics in the literature.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.OA-2018-0036}, url = {http://global-sci.org/intro/article_detail/nmtma/12913.html} }
TY - JOUR T1 - An Optimized Two-Step Hybrid Block Method Formulated in Variable Step-Size Mode for Integrating $y''=f(x,y,y')$ Numerically JO - Numerical Mathematics: Theory, Methods and Applications VL - 2 SP - 640 EP - 660 PY - 2018 DA - 2018/12 SN - 12 DO - http://doi.org/10.4208/nmtma.OA-2018-0036 UR - https://global-sci.org/intro/article_detail/nmtma/12913.html KW - AB -

An optimized two-step hybrid block method is presented for integrating general second order initial value problems numerically. The method considers two intra-step points which are selected adequately in order to optimize the local truncation errors of the main formulas for the solution and the first derivative at the final point of the block. The new proposed method is consistent, zero-stable and has seventh algebraic order of convergence. To illustrate the performance of the method, some numerical experiments are presented for solving this kind of problems, in comparison with methods of similar characteristics in the literature.

Gurjinder Singh & Higinio Ramos. (2020). An Optimized Two-Step Hybrid Block Method Formulated in Variable Step-Size Mode for Integrating $y''=f(x,y,y')$ Numerically. Numerical Mathematics: Theory, Methods and Applications. 12 (2). 640-660. doi:10.4208/nmtma.OA-2018-0036
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