Derivation of block LMM methods for the direct solution of Higher ODEs

Some self starting Discrete Methods and Hybrid Block Methods of High Orders were constructed for solution of General Second and Third Order Initial Value Problems directly without reducing it to its equivalent first Order systems of Ordinary Differential Equations. The continuous formulations in each of the proposed integrator enabled us to differentiate and evaluate at some grid and off- grid points to take care of and in the Method. Also the Methods could equally handled Special cases of ODEs directly. Also derived was the new Method of obtaining Order and Error constants for Third Order Linear Multi-step Methods
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