# Optimization of two-step block method with three hybrid points for solving third order initial value problems

Volume 12, Issue 7, pp 450--469 Publication Date: March 09, 2019       Article History
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### Authors

Bothayna S. H. Kashkari - Department of Mathematics, Faculty of Science, University of Jeddah, Jeddah, Saudi Arabia. Sadeem Alqarni - Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia. - Department of Mathematics, Faculty of Science, Al-Baha University, Al-Baha, Saudi Arabia.

### Abstract

An optimized two-step hybrid block method for the numerical solution of third-order initial value problems is presented. The method takes into regard three hybrid points which are selected suitably to optimize the local truncation errors of the main formulas for the block. The method is zero-stable and consistent with sixth algebraic order. Some numerical examples are debated to demonstrate the efficiency and the accuracy of the proposed method.

### Keywords

• Two-step hybrid block method
• third-order initial value problems
• stability
• consistent

•  34A38
•  65C20
•  93C30

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