A Second Derivative Simpson's Method for Solving Initial Value Problems with Stiff

Collocation and interpolation of power series approximation solution is used to develop a continuous hybrid Second Derivative of Simpson's scheme with four off-grid points for the solution of the Stiff System of ordinary differential equations (ODEs). Evaluating the continuous scheme at various grid and off-grid points, the discrete schemes are obtained and written in block form. The block method's fundamental characteristics, including order, zero stability, and stability region, were examined. After testing the block method on a few numerical instances, it was discovered to provide a better approximation than comparable methods reported in the literature.