Abstract
Finite difference schemes of exponential and polynomial orders for solving the model problem a(x)y + b(x)y′ = g(x, y) are obtained. A scheme of order h 2 is obtained usingone evaluation of g at x i while a scheme of order h 4 is obtained using three evaluations of g at the nodal points x i− 1 , x i, x i+ 1 . Convergence of some of the schemes is shown. Computational results exhibit the required order
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