Backward differentiation formulae with variable stepsize variable order for solving stiff delay differential equations / Nora Baizura Mohd Isa

This thesis describes the development of predictor-corrector variable stepsize variable order based on backward differentiation formulae (BVSVO) method and direct predictor-corrector variable stepsize variable order based on backward differentiation formulae (DBVSVO) method for solving first order and special second order stiff delay differential equations respectively. The predictor and corrector formulae are represented in divided difference form. The developed methods are implemented using variable stepsize variable order technique. In varying the stepsize, the coefficients of the methods need to be recomputed at every step which will create extra computational cost. Thus, in order to reduce the computational cost, the coefficients of the methods are computed by a simple recurrence relation. In solving first order stiff delay differential equations using the BVSVO method, the numerical results are compared with non-stiff method, single-step method and multistep method.From the numerical results, the BVSVO method has shown the efficiency and reliability for solving first order stiff delay differential equations in terms of total number of steps, maximum error and average error. The DBVSVO method is used to solve special second order stiff delay differential equations directly without reducing to first order equations. We present some test examples to check an accuracy and efficiency of the DBVSVO method. For comparison purposes, the same set of test examples is reduced to a system of first order equations and solved using the BVSVO method. The numerical results for solving special second order stiff delay differential equations using the DBVSVO method is better compared with the BVSVO method in term of total number of function evaluations