An integral inequality and the Ricatti-Bernoulli differential equation
Mark B. Villarino
TL;DR
This paper introduces a new integral inequality to rigorously estimate the accuracy of partial sum approximations for solutions to the Ricatti-Bernoulli differential equation.
Contribution
It presents a novel integral inequality method for providing a priori error bounds in the power series solutions of Ricatti-Bernoulli equations.
Findings
Established a rigorous a priori error estimate for power series solutions.
Demonstrated the effectiveness of the integral inequality in bounding approximation errors.
Applied the method specifically to the Ricatti-Bernoulli differential equation.
Abstract
We apply an integral inequality to obtain a rigorous \emph{a priori} estimate of the accuracy of the partial sum to the power series solution of the Ricatti-Bernoulli differential equation.
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Taxonomy
TopicsMathematical functions and polynomials