The Second Order Adaptive Moving Mesh Method for a Singularly Perturbed Fredholm Integro-Differential Equation

doi:10.13438/j.cnki.jdzk.2024.04.004

Abstract

Abstract: An exponentially fitted finite difference scheme constructed by the base function method and the compound trapezoidal formula is applied to make discrete a class of singularly perturbed Fredholm integral differential equation.Combining the truncation error estimate,the boundary estimate and the stability analysis,the second order uniform convergence in the infinity norm with respect to the perturbation parameter for the adaptive moving mesh method is proved.Based on the above theoretical analysis,the algorithm to produce the mesh is designed.

Key words: singularly perturbed problem, Fredholm integral equation, adaptive moving mesh, uniform convergence

LUO Dan, MAO Zhi. The Second Order Adaptive Moving Mesh Method for a Singularly Perturbed Fredholm Integro-Differential Equation[J]. Journal of Jishou University(Natural Sciences Edition), 2024, 45(4): 15-25.

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