2024 : 11 : 13
Ali Shokri Shokri

Ali Shokri Shokri

Academic rank: Professor
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Education: PhD.
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Faculty: 1
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Research

Title
Second Derivative Block Hybrid Methods for the Numerical Integration of Differential Systems
Type
JournalPaper
Keywords
block hybrid method; continuous scheme; differential system; multistep collocation
Year
2022
Journal Fractal and Fractional
DOI
Researchers Dauda Gulibur Yakubu ، Ali Shokri Shokri ، Geoffrey Micah Kumleng ، Daniela Marian

Abstract

The second derivative block hybrid method for the continuous integration of differential systems within the interval of integration was derived. The second derivative block hybrid method maintained the stability properties of the Runge–Kutta methods suitable for solving stiff differential systems. The lack of such stability properties makes the continuous solution not reliable, especially in solving large stiff differential systems. We derive these methods by using one intermediate off-grid point in between the familiar grid points for continuous solution within the interval of integration. The new family had a high accuracy, non-overlapping piecewise continuous solution with very low error constants and converged under the suitable conditions of stability and consistency. The results of computational experiments are presented to demonstrate the efficiency and usefulness of the methods, which also indicate that the block hybrid methods are competitive with some strong stability stiff integrators.