**AUTHORS:**Grace O. Akinlabi, Raphael B. Adeniyi

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**ABSTRACT:**
Hybrid Boundary Value Methods (HyBVMs) are a new class of Boundary Value Methods (BVMs)
proposed recently for the approximation of Ordinary Differential Equations (ODEs). These new schemes
behave just like the BVMs as the HyBVMs are also based on the Linear Multistep Methods (LMMs) but
utilizes data at both step and off-step points. Numerical tests on both linear and nonlinear Boundary Value
Problems (BVPs) were presented using the HyBVMs of order 6 and order 4. The results were compared with
the symmetric schemes: Extended Trapezoidal Rules (ETRs) of order 6 and order 4.

**KEYWORDS:**
Boundary value methods, hybrid BVMs, boundary value problems, linear multistep method,
numerical methods for ODEs.

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