Half-Sweep Refinement of SOR Iterative Method via Linear Rational Finite Difference Approximation for Second-Order Linear Fredholm Integro-Differential Equations

The numerical solutions of the second-order linear Fredholm integro-differential equations have been considered and discussed based on several discretization schemes. In this paper, new schemes are developed derived hybrid three-point half-sweep rational finite difference (3HSLRFD) approaches with composite trapezoidal (HSCT) approach. main advantage established is that they discretize differential terms integral term into algebraic generate corresponding system. Furthermore, (HS) concept combined refinement successive over-relaxation (RSOR) iterative method to create (HSRSOR) method, which implemented get solution a system equations. Apart from that, classical or full-sweep Gauss-Seidel (FSGS) (FSSOR) methods presented, serve as control in paper. end, we employed FSGS, FSRSOR HSRSOR obtain three examples make detailed comparison aspects number iterations, elapsed time maximum absolute error. Numerical results demonstrate lesser faster time, more accurate than FSGS. addition, most effective methods. To sum up, paper has successfully proposed applicability superiority 3HSLRFD-HSCT