Coupled block method for solving ordinary and delay differential equations

The idea of this thesis is to introduce two numerical methods which are known as coupled block methods for solving first order Ordinary Differential Equations (ODEs) using variable step size and order. The methods consist of two block methods which were presented as in the simple form of the Adams Moulton type. Next, the methods were implemented for solving Delay Differential Equations (DDEs) using variable step size and order. The delay term was approximated using divided difference interpolation. The stability properties of the developed block methods when applied to ODEs and DDEs were studied and their regions of stability were presented. The numerical results showed that the performance of the proposed methods are acceptable in terms of total number of steps, maximum error and execution time for solving first order ODEs and DDEs using variable step size and order. In conclusion, the methods were competitive and suitable for solving ODEs and DDEs

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