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Abstract
In this thesis, we present a class of new spline collocation methods for solving initial value problems in ordinary, delay and algebraic differential equations including stiff equations 0 These methods are based on seventh C3- spline collocation schemes with four collocation points xi-1+a = xi-1 + ah, xi-1+b = xi-1 + bh, xi-1+q = xi-1 + qh and xi = xi-1 + h in each subinterval [xi-1,xi], i= 1(1)N, where a, b, q I(0,1). Some of the results in the thesis have been published in some of external journals.