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Description

One of the major issues in numerical analysis/scientific computing is the accuracy of the underlying numerical methods. It is a common knowledge that the accuracy of all current numerical methods for differentiation, integration, ordinary and partial differential er order accurate approximations for differentiation, integration, ODEs, and PDEs when the underlying approximated functions are not smooth. The key idea of this work is the introduction of the rate of corrections which is a universality, quantifies the accuracy of the numerical method used, and is computationally feasible. The rate of corrections is then used to increase the accuracy of the approximation. Also, this approach can be applied to problems without continuum background such as the sequence of period-doubling bifurcations in chaos.