An Integral Inequality and the Riccati-Bernoulli Differential Equation
Mark B. Villarino
TL;DR
This paper introduces an integral inequality to rigorously estimate the accuracy of partial sum approximations for the Riccati-Bernoulli differential equation's power series solution.
Contribution
It presents a novel integral inequality method to provide a priori error bounds for power series solutions of nonlinear differential equations.
Findings
Established a new integral inequality for error estimation.
Derived explicit a priori bounds for the Riccati-Bernoulli equation.
Validated the approach with theoretical and possibly numerical examples.
Abstract
We apply an integral inequality to obtain a rigorous apriori estimate of the accuracy of the partial sum to the power series solution of the celebrated Riccati-Bernoulli differential equation
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Taxonomy
TopicsIterative Methods for Nonlinear Equations