Order-Optimal Numerical Methods for Solving Singular Integro-Differential Equations

Key Points

• This research aims to develop and verify numerical methods for solving singular integro-differential equations efficiently.
• Studied linear integro-differential equation with a singular differential operator.
• Proposed generalized methods of moments and subdomains for approximate solutions.
• Analyzed solutions within the framework of generalized functions.
• Established the optimality of the proposed methods regarding accuracy.
• Demonstrated improved accuracy in solving singular integro-differential equations.

Abstract