Abstract
We study a new sixth-order compact discretization using uniform three-grid point for the mildly nonlinear differential equation $$\phi ''=g(t,\phi )$$ , subject to the values of ϕ given at two end points of the regular solution interval. We also discuss three-step AGE (THAGE) iteration method as an application to the resulting difference equation as a powerful numerical computation device. In this algorithm, the common term is evaluated first to save the CPU time in comparison with the corresponding two-step algorithm. In addition, the error analysis is studied. Numerical performance is compared with the exact solution, and with the two-step AGE and SOR iteration methods.
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