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September 16, 2025Mathematica PannonicaOpen Access

Global Error Propagation in the Numerical Solution of an Ordinary Differential Equation with a Discontinuity

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Error propagates through numerical solutions following a discontinuity, affecting accuracy and reliability.
An analytical expression for error was derived, revealing terms that could only be controlled before the discontinuity.
A condition number was identified that may amplify the location error significantly.
An example was presented to demonstrate error effects and propagation in practice.

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This analysis examines error propagation in numerical solutions for ordinary differential equations, suggesting risk from discontinuity locations.

J.S.C. Prentice (2025) studied this question.

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This analysis examines error propagation in numerical solutions for ordinary differential equations, suggesting risk from discontinuity locations.