Development of Exponential Linear Multistep Methods for the Solution of First-Order Ordinary Differential Equations

Several approaches have been applied by different researchers to produce linear multistep methods (LMMs) for the solution of ordinary differential equations (ODEs). In this paper, some LMMs have been developed via the collocation and interpolation technique using the exponential function as the basis function. The continuous and discrete forms of the methods have been evaluated and tested on some first-order ordinary differential equations. Results are presented in terms of maximum absolute errors and have shown that the proposed methods produce more accurate approximations than the existing LMMs derived using some other polynomial functions. We therefore recommend that the proposed methods should be tested on ODEs of second and higher orders.