A novel variant of weighted quadratic mean iterative methods for Fredholm integro-differential equations - Ng, Wei Li; Elayaraja Aruchunan; Zailan Siri (Penerbit Universiti Kebangsaan Malaysia, 2025)
Integro-differential equations are critical for modelling real-world phenomena in physics, engineering, and biology. This paper introduces a Quadratic Mean iterative method to solve dense linear systems derived from the discretization of second and fourth-order Fredholm integro-differential equations (FIDEs). The solution of the FIDEs is approximated using finite difference, composite trapezoidal, and composite Simpson’s 1/3 and 3/8 schemes. The quadratic mean iterative method then solves the discretized system with different mesh sizes. As the resulting systems are large, a complexity reduction approach is implemented on the quadratic mean method to develop the half-sweep quadratic mean iterative method. The newly proposed iterative method includes a novel theorem, comprehensive proofs, and a detailed convergence analysis. The numerical results indicate that the quadratic mean method significantly outperforms the Gauss-Seidel iterative method in terms of efficiency, making it a promising solution for FIDEs.