Numerical treatment for multi-pantograph integro-differential equation via tau spectral method

Pantograph integro-differential equations have many crucial applications in science and engineering. The presence of differential behavior, scaling, and memory effects makes pantograph integro-differential equations capable of describing complex systems in control theory and mathematical biology. In this paper, we provide a numerical approach to the multi-pantograph integro-differential equation. The Jacobi tau spectral approach is utilized with the help of differential, integral, and pantograph operational matrices to solve one- and two-dimensional linear multi-pantograph integro-differential equations. The high accuracy, convergence, and simplicity motivate one to apply the tau spectral approach to the problem studied. Numerical results for two test problems are performed to test the validity and superiority of the suggested numerical scheme over other numerical schemes.