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k -STEP BLOCK HYBRID METHOD FOR NUMERICAL APPROXIMATION OF FOURTH-ORDER ORDINARY DIFFERENTIAL EQUATIONS
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  • Faruk Muritala,
  • AbdulAzeez K. Jimoh,
  • Muideen Ogunniran,
  • Abdulmalik A. Oyedeji,
  • J.O. LAWAL
Faruk Muritala
Kwara State University

Corresponding Author:[email protected]

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AbdulAzeez K. Jimoh
Kwara State University
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Muideen Ogunniran
Osun State University
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Abdulmalik A. Oyedeji
Federal University of Technology Minna
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J.O. LAWAL
Kwara State University
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Abstract

Conventionally, the method of solving fourth-order initial value problems of an ordinary differential is to first reduce it to a system of first-order differential equations. This approach affects the effectiveness and convergence of the numerical method as a result of the transformation. This paper comprises of the derivation, analysis, and implementation of a new hybrid block method which is derived by collocation and interpolation of an assumed basis function. The basic properties of the block method including zero stability, error constants, consistency, order, and convergence were analyzed. From the analysis, the block method derived was found to be zero-stable, consistent, and convergent. Also, the block method was tested on some numerical examples and the result computed shows that the derived schemes are more accurate than existing methods in the literature.