SOLVING OF VOLTERRA INTEGRO-DIFFERENTIAL EQUATIONS OFTHE SECOND KIND USING BLOCK HYBRID METHOD

Authors

  • Ezekiel Olaoluwa OMOLE
    Federal University of Technology and Environmental Sciences, Iyin-Ekiti 362005, Ekiti State, Nigeria
  • Taiwo Stephen Fayose
    Federal Polytechnic Ado-Ekiti, Ekiti State, Nigeria
    Federal University of Technology and Environmental Sciences, Iyin-Ekiti 362005, Ekiti State, Nigeria
  • Folasade Helen Odeniyan-Fakuade
    Osun State University, Osogbo, Osun State, Nigeria
  • Bamikole Gbenga Ogunware
    Adekunle Ajasin University, Akungba-Akoko, Ondo State, Nigeria
  • Olanrewaju Thomas Olotu
    University of Ilorin, Kwara State, Nigeria
  • Taiwo Aanu Ogunlusi
    Federal University Oye-Ekiti, Ekiti State, Nigeria
  • Taiwo Eniola Fayode
    Bamidele Olumilua University of Education, Science and Technology, Ikere-Ekiti, Ekiti State, Nigeria

Keywords:

BHM , VIDEs , Second kind , LBA , Consistency , Numerical simulation , Power series polynomial , Convergence analysis

Abstract

This study presented a Block Hybrid Method (BHM) for numerical integration of linear and nonlinear Volterra Integro-Differential Equations (VIDEs) of the second kind. The BHM was derived using the linear multistep method with the Linear Block Algorithm (LBA) to obtain a new block algorithm and its higher derivatives. Numerically, the analysis of the basic properties of the BHM was studied and found to be of uniform order seven, consistency, zerostability, and convergence, with an A-stable region of absolute stability. The numerical simulation of BHM was carried out by integrating the BHM on linear and nonlinear Volterra integro-differential equations of second kind. The results obtained were compared with existing methods and presented in tables and graphically shown. The numerical comparisons show that the BHM produces highly accurate approximations and minimize the truncation error over the existing methods. The study shows that the BHM is efficient, stable and suitable for solving Volterra integro-differential equations of the second kind.

Author Biographies

Ezekiel Olaoluwa OMOLE

Department of Mathematics

Taiwo Stephen Fayose

Department of Statistics
Department of Mathematical Sciences

Folasade Helen Odeniyan-Fakuade

Department of Mathematics

Bamikole Gbenga Ogunware

Department of Mathematical Sciences

Olanrewaju Thomas Olotu

Department of Mathematics

Taiwo Aanu Ogunlusi

Department of Mathematics

Taiwo Eniola Fayode

Department of Mathematical Sciences

Dimensions

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Published

30-06-2026

How to Cite

SOLVING OF VOLTERRA INTEGRO-DIFFERENTIAL EQUATIONS OFTHE SECOND KIND USING BLOCK HYBRID METHOD. (2026). FULafia Journal of Science and Technology , 10(2), 154-164. https://doi.org/10.62050/fjst2026.v10n2.796

Issue

Vol. 10 No. 2 (2026): Fulafia Journal of Science and Technology (FJST)

Section

Physical Sciences
Copyright & Licensing

How to Cite

SOLVING OF VOLTERRA INTEGRO-DIFFERENTIAL EQUATIONS OFTHE SECOND KIND USING BLOCK HYBRID METHOD. (2026). FULafia Journal of Science and Technology , 10(2), 154-164. https://doi.org/10.62050/fjst2026.v10n2.796

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