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

For solving first order delay differential equations without using interpolation techniques in determining the delay argument, the third derivative block backward differentiation formulae were created. A reasonable idea of sequence was used to analyse the delay argument. 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 help of the matrix inversion formula. The schemes that resulted were created using their own continuous systems. These discrete schemes' order and error constants, zero stability, convergent, and region of absolute stability were all calculated. N-stability and M-stability were also looked into. When compared to their exact solutions and other existing methods, the scheme for step number k = 4 performed better and faster in terms of efficiency, accuracy, 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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