HYBRID BLOCK METHOD TO SOLVING FIRST ORDER INITIAL VALUE PROBLEM IN ORDINARY DIFFERENTIAL EQUATIONS

Resumo

This study examines the hybrid block method (HBM) derivation for solving first order initial
value problems (FOIVP) in ordinary differential equations (ODEs). Using the collocation and interpolation
procedure at equally spaced locations in the interval of consideration, a continuous formula is generated from
the estimated answer, which is assumed to be in the form of power series. The accuracy of the procedure is
significantly influenced by the advantage of using data off-step points. The efficacy of the suggested approach
is demonstrated by a few numerical examples that show how close the answers are to the precise solutions.
All types of FOIVP involving ODEs can be solved utilizing this method.