IMPLEMENTATION OF THIRD DERIVATIVE BLOCK BACKWARD DIFFERENTIATION FORMULAE FOR SOLVING FIRST ORDER DELAY DIFFERENTIAL EQUATIONS WITHOUT INTERPOLATION TECHNIQUES
B. O. OSU *
Department of Mathematics, Michael Okpara University of Agriculture, Umudike, Nigeria.
C. CHIBUISI
Department of Insurance, University of Jos, Jos, Nigeria.
N. N. OKWUCHUKWU
Department of Science and Technology Education, University of Jos, Jos, Nigeria.
C. OLUNKWA
Department of Mathematics, Abia State University, Uturu, Nigeria.
N. A. OKORE
School of Sciences, Abia State College of Education Technical, P.M.B. 100, Arochukwu, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
The third derivative block backward differentiation formulae was developed for solving first order delay differential equations without the implementation of interpolation techniques in estimating the delay argument. The delay argument was evaluated using a satisfactory concept of sequence. The development of the continuous system of these block methods was worked-out through the use of Third Derivative Block Backward Differentiation Formulae Method with the help of linear multistep collocation procedure by matrix inversion formula. The resulting schemes were established through their individual continuous systems. The order and error constants, zero stability, convergent and region of absolute stability of these discrete schemes were worked-out. The N-stability and M-stability were also investigated. The analysis of the absolute error results showed that 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 when compared with their exact solutions and other existing methods.
Keywords: First order delay differential equations, third derivative backward differentiation formulae, block method.