The original idea presented in this article is the application of a shifted Legendre pseudospectral (SLP) scheme for solving delay integral equations (DIEs). We first reformulate the DIE as a continuous-time optimization problem. Next, we employ the SLP scheme to discretize the problem and convert it into a nonlinear programming (NLP) problem. By solving the resulting NLP, approximate solutions to the original DIE are obtained. The convergence of the proposed scheme is proved. Furthermore, numerical results are included to demonstrate both the superiority of the scheme over some existing methods and its overall effectiveness.
mahmoudi, M. (2026). A convergent numerical scheme for delay integral equations. (e742144). Mathematics and Computational Sciences, (), e742144 https://doi.org/10.30511/mcs.2026.2079842.1650
MLA
mahmoudi, M. "A convergent numerical scheme for delay integral equations" .e742144 , Mathematics and Computational Sciences, , 2026, e742144. doi: 10.30511/mcs.2026.2079842.1650
HARVARD
mahmoudi M. (2026). 'A convergent numerical scheme for delay integral equations', Mathematics and Computational Sciences, (), e742144. doi: 10.30511/mcs.2026.2079842.1650
CHICAGO
M. mahmoudi, "A convergent numerical scheme for delay integral equations," Mathematics and Computational Sciences, (2026): e742144, doi: 10.30511/mcs.2026.2079842.1650
VANCOUVER
mahmoudi M. A convergent numerical scheme for delay integral equations. MCS. 2026;():e742144. doi: 10.30511/mcs.2026.2079842.1650
