IMPLEMENTATION OF THIRD DERIVATIVE BLOCK BACKWARD DIFFERENTIATION FORMULAE FOR SOLVING FIRST ORDER..

For solving first order delay differential equations without using interpolation techniques in estimating the delay argument, the third derivative block backward differentiation formulae were developed. A suitable definition of series was used to test the delay statement. The continuous system of these block methods was developed using the Third Derivative Block Backward Differentiation Formulae Method and a linear multistep collocation procedure with the aid of the matrix inversion formula. The schemes that resulted were created using their own continuous systems. Zero stability, order and error constants These discrete schemes' convergent and absolute stability regions were determined. N-stability and M-stability were also looked at.As compared to their exact solutions and other existing methods, the scheme for step number k = 4 performed better and faster in terms of performance, precision, consistency, convergence, region of absolute stability, and Central Processing Unit Time (CPUT) at fixed step size than the schemes for step numbers k = 3 and 2.

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