This paper presents the comparison of the two Adams methods using extrapolation for the best method suitable for the approximation of the solutions. The two methods (Adams Moulton and Adams Bashforth) of step k = 3 to k = 4 are considered and their equations derived. The extrapolation points, order, error constant, stability regions were also derived for the steps. More importantly, the consistency and zero stability are also investigated and finally, the derived equations are used to solve some non-stiff differential equations for best in efficiency and accuracy.

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This paper presents the comparison of implicit scheme and modied implicit scheme for solving parabolic partial dierential equations, the modied implicit scheme is compared with the implicit scheme using its stability, local truncation error, derivation and numerical examples. Following this, it was discovered that the modied implicit scheme can be used as an alternative scheme to the implicit scheme for solving problems on parabolic partial dierential equations.