Abstract
Abstract We present an Extended Continuous Block Backward Differentiation Formula (ECBBDF) of order k+1 for the numerical solution of stiff ordinary differential equations. This is achieved by constructing an Extended Continuous Backward Differentiation formula (ECBDF) together with the additional methods from its first derivative and are combined to form a single block of methods that simultaneously provide the approximate solutions for the stiff Initial Value Problems (IVPs). The error constant and stability property of the (ECBBDF) is discussed. We use the specific cases k = 4 and k = 5 to illustrate the process. The performance of the method is demonstrated on some numerical examples to show the accuracy and efficiency advantages of the method.
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