Raihanatu MuhammadAbdulmalik Oyedeji2025-04-152024-112321-9653http://repository.futminna.edu.ng:4000/handle/123456789/695International Journal for Research in Applied Science & Engineering Technology (IJRASET) ISSN: 2321-9653; IC Value: 45.98; SJ Impact Factor: 7.538 Volume 12 Issue XI Nov 2024- Available at www.ijraset.comIn this paper, the theory of linear transformation (Homomorphism) and monomorphism is applied to a first-order Runge-Kutta Type Method illustrated in a Butcher Table and the extended second order Runge- Runge-Kutta type Method to substantiate their uniform order and error constants obtained. A homomorphism is a mapping from one group to another group which preserves the group operations. It’s sometimes called the operation preserving function. The methods which initially are Linear Multistep were reformulated into Runge-Kutta (R-K) Type to establish the advantages the R-K has over Linear Multistep. The first-order Linear multistep was reformulated into first-order R-K type which was further extended to second order. This extension can be made to higher order. For this study, the extension was limited to the second order.enLinear transformationMonomorphismImplicitRunge-Kutta typeArticle