In this paper, we develop a numerical resolution of the space-time fractional advection-dispersion equation. We utilize spectral-collocation method combining with a product integration technique in order to discretize the terms involving spatial fractional order derivatives that leads to a simple evaluation of the related terms. By using Bernstein polynomial basis, the problem is transformed in...

In this article, we develop numerical schemes for solving stiff reaction-diffusion equations on annuli based on Chebyshev and Fourier spectral spatial discretizations and integrating factor methods for temporal discretizations. Stiffness is resolved by treating the linear diffusion through the use of integrating factors and the nonlinear reaction term implicitly. Root locus curves provide a suc...

This work is about the use of some classical spectral collocation methods as well with new software system Chebfun in order to compute eigenpairs high Sturm–Liouville eigenproblems. The analysis divided into two distinct directions. For problems clamped boundary conditions, we preconditioning differentiation matrices and for hinged end conditions equation transformed a second then conventional ...

In this manuscript, we solve the ordinary model of nonlinear smoking mathematically by using second kind shifted Chebyshev polynomials. The stability equilibrium point is calculated. schematic illustrates our proposition. We discuss optimal control model, and formularize work through necessary optimality cases. A numerical technique for simulation problem adopted. Moreover, a method presented, ...