Limit distributions of the Pearson statistics for nonhomogeneous polynomial scheme

For a nonhomogeneous polynomial scheme, conditions are found under which the Pearson statistic distributions converge to the distribution of nonnegative quadratic form of independent random variables with the standard normal distribution.

Analysis of the Generalized Inverse Polynomial Scheme to Initial Value Problems

In this paper, we study the analysis of the generalized inverse polynomial scheme for the numerical solution of initial value problems of ordinary differential equation. At first, we generalize the scheme up to the fifth stage using the Binomial expansion and Taylor’s series method towards its derivation. The trend shows the generalization to the kth term. The analysis demonstrates the efficiency and the effectiveness of the generalized scheme.Keywords— Taylor’s Series, Initial Value Problem, Stability, Consistency, Convergence.