TY - JOUR
T1 - Hybrid Block Method for Direct Integration of First, Second and Third Order IVPs
AU - Adeyefa, Emmanuel
AU - Olagunju, Adeyemi
PY - 2021
DA - May
JF - Cankaya University Journal of Science and Engineering
JO - CUJSE
PB - Cankaya University
WT - DergiPark
SN - 2564-7954
SP - 1
EP - 8
VL - 18
IS - 1
LA - en
AB - Construction of numerical methods for the solution of initial value problems (IVPs) in ordinary differential equations (ODEs) has been considered overwhelmingly in literature. However, the use of a single numerical method for the integration of ODEs of more than one order has not been commonly reported. In this paper, we focus on the development of a numerical method capable of obtaining the numerical solution of first, second and third-order IVPs. The method is formulated from continuous schemes obtained via collocation and interpolation techniques and applied in a block-by-block manner as a numerical integrator for first, second and third-order ODEs. The convergence properties of the method are discussed via zero-stability and consistency. Numerical examples are included and comparisons are made with existing methods in the literature.
KW - Consistency
KW - Convergence
KW - Zero-Stability
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UR - https://dergipark.org.tr/en/pub/cankujse/issue/61974/745271
L1 - https://dergipark.org.tr/en/download/article-file/1126132
ER -