A kernel-based method for Volterra delay integro-differential equations

Abstract

Volterra integro-differential equations with constant delay $\tau>0$ are presented in this paper. We used a numerical method based on reproducing kernels to investigate well-known equations. The convergence analysis of the utilized approach is taken into account, which also provides the theoretical structure of the method. In addition, we derive some effective error estimates for the proposed method when applied to Volterra delay integro differential equations. Numerical experiments are carried out to illustrate the efficiency and applicability of the proposed method.

Keywords

• Volterra integro-differential equations
• delay arguments
• reproducing kernel Hilbert space
• convergence analysis
• error estimate

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