@article{article_524218, title={A generalized operational method for solving integro–partial differential equations based on Jacobi polynomials}, journal={Hacettepe Journal of Mathematics and Statistics}, volume={45}, pages={311–335}, year={2016}, author={Borhanifar, Abdollah and Sadri, Khadijeh}, keywords={Best approximation,Collocation method,Integro–partial differential equations,Operational matrix,Shifted Jacobi polynomials}, abstract={In this paper, a numerical method is developed for solving linear and
nonlinear integro-partial differential equations in terms of the two variables Jacobi polynomials. First, some properties of these polynomials
and several theorems are presented then a generalized approach implementing a collocation method in combination with two dimensional
operational matrices of Jacobi polynomials is introduced to approximate the solution of some integro–partial differential equations with
initial or boundary conditions. Also, it is shown that the resulted approximate solution is the best approximation for the considered problem. The main advantage is to derive the Jacobi operational matrices
of integration and product to achieve the best approximation of the
two dimensional integro–differential equations. Numerical results are
given to confirm the reliability of the proposed method for solving these
equations.}, number={2}, publisher={Hacettepe University}