45J05 Integro-ordinary differential equations

Overview

This topic studies integro-ordinary differential equations in the setting of integro-ordinary differential equations, with emphasis on foundational results, operator behavior, and analytic applications.

Related Wikipedia Page

Integrodifferential equation (Wikipedia)

Useful Links

• Integrodifferential equation (Wikipedia)
• Volterra equation (Wikipedia)
• Initial value problem (Wikipedia)

Key Ideas

• Structural properties of the underlying analytic objects
• Continuity, boundedness, and convergence principles
• Interaction between abstract theory and computational/application contexts

Typical Uses

Used in research and advanced applications involving integro-ordinary differential equations, including representation, solvability, and stability analysis.

Applications

• Functional and harmonic analysis
• Operator and algebraic methods
• Mathematical physics and PDE models

References

• Gripenberg, G., Londen, S.-O., and Staffans, O. (1990). Volterra Integral and Functional Equations. Cambridge: Cambridge University Press.
• Brunner, H. (2004). Collocation Methods for Volterra Integral and Related Functional Differential Equations. Cambridge: Cambridge University Press.
• Recent journal-paper search for Integro-ordinary differential equations

Recommended Textbooks

• Gripenberg, G., Londen, S.-O., and Staffans, O. (1990). Volterra Integral and Functional Equations. Cambridge: Cambridge University Press.
• Brunner, H. (2004). Collocation Methods for Volterra Integral and Related Functional Differential Equations. Cambridge: Cambridge University Press.