Block backward differentiation methods for single delay differential equations - Heng, Siaw Ching (2012)
This thesis concerns mainly in modifying existence method of Block Backward Differentiation Formulas (BBDFs) for solving stiff single Delay Differential Equations (DDEs). The method involved will solve the first order single DDEs using constant stepsize. The general equation for single DDEs is given as follows showed the method gave good results in term in maximum error and comparable results in term of execution time. In addition, the stability region of BBDFs method is obtained and it is applied to solve DDEs. The illustrations of the stability region are presented. In conclusion, the Block Backward Differentiation Formulas method is appropriate for solving the first order stiff single Delay Differential Equations. [formula] The method is adapted with Newton Divided Difference interpolation to approximate delay term. The performance of 2-point BBDFs method and 3-point BBDFs method is compared with classical 1-point Backward Differentiation Formulas (BDFs). The source code is written in C language. Numerical results showed the method gave good results in term in maximum error and comparable results in term of execution time. In addition, the stability region of BBDFs method is obtained and it is applied to solve DDEs. The illustrations of the stability region are presented. In conclusion, the Block Backward Differentiation Formulas method is appropriate for solving the first order stiff single Delay Differential Equations