Development and Analysis of Block Methods for Solving Holomorphic Complex First-Order Ordinary Differential Equations
DOI:
https://doi.org/10.33003/fjs-2026-1012-5239Keywords:
Complex first-order, Holomorphic, Linear, Non-Linear ODEsAbstract
This study presents the development and analysis of Block Linear Multistep Methods (BLMM) for solving complex first-order ordinary differential equations (ODEs) involving linear and non-linear holomorphic functions. Two distinct block schemes, formulated on grids with and nodes, are derived using collocation techniques. The basic properties of the method such as order, error constant, zero stability, consistency and convergence are investigated. The numerical results demonstrate that both schemes achieve accuracy, with errors reaching as low as. Specifically, the method of scheme consistently achieves faster convergence and lower absolute errors.
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Copyright (c) 2026 Hamza Yusuf Abdullahi; Ademola M. Badmus
This work is licensed under a Creative Commons Attribution 4.0 International License.
