Hamad Talibi Alaoui

Bio: Hamad Talibi Alaoui is an academic researcher. The author has contributed to research in topics: Matrix (mathematics) & Krylov subspace. The author has an hindex of 2, co-authored 4 publications receiving 10 citations.

Global extended Krylov subspace methods for large-scale differential Sylvester matrix equations

Abstract: In this paper, we present a new numerical methods for solving large-scale differential Sylvester matrix equations with low rank right hand sides. These differential matrix equations appear in many applications such as robust control problems, model reduction problems and others. We present two approaches based on extended global Arnoldi process. The first one is based on approximating exponential matrix in the exact solution using the global extended Krylov method. The second one is based on a low-rank approximation of the solution of the corresponding Sylvester equation using the extended global Arnoldi algorithm. We give some theoretical results and report some numerical experiments to show the effectiveness of the proposed methods compared with the extended block Krylov method given in Hached and Jbilou (Numer Linear Algebra Appl 255:e2187, 2018).

The extended block Arnoldi method for solving generalized differential Sylvester equations

Abstract: In the present paper, we propose a new method for solving large-scale generalized differential Sylvester equations, by projecting the initial problem onto the extended block Krylov subspace with an orthogonality Galerkin condition. This projection gives rise to a low-dimensional generalized differential Sylvester matrix equation. The low-dimensional equations is then solved by Rosenbrock or BDF method. We give some theoretical results and report some numerical experiments to show the effectiveness of the proposed method.

Numerical methods for solving large-scale systems of differential equations

Abstract: In this paper, we propose two new methods to solve large-scale systems of differential equations, which are based on the Krylov method. In the first one, the exact solution with the exponential projection technique of the matrix. In the second, we get a new problem of small size, by dropping the initial problem, and then we solve it in ways, such as the Rosenbrock and the BDF. Some theoretical results are presented such as an accurate expression of the remaining criteria. We give an expression of error report and numerical values to compare the two methods in terms of how long each method takes, and we also compare the approaches.

Existence of Solutions for Unbounded Elliptic Equations with Critical Natural Growth

Abstract: We investigate existence and regularity of solutions to unbounded elliptic problem whose simplest model is {-div[(1+uq)∇u]+u=γ∇u2/1+u1-q+f in Ω, u=0 on ∂Ω,}, where 0<q<1, γ>0 and f belongs to some appropriate Lebesgue space. We give assumptions on f with respect to q and γ to show the existence and regularity results for the solutions of previous equation.

The extended block Arnoldi method for solving generalized differential Sylvester equations

Abstract: In the present paper, we propose a new method for solving large-scale generalized differential Sylvester equations, by projecting the initial problem onto the extended block Krylov subspace with an orthogonality Galerkin condition. This projection gives rise to a low-dimensional generalized differential Sylvester matrix equation. The low-dimensional equations is then solved by Rosenbrock or BDF method. We give some theoretical results and report some numerical experiments to show the effectiveness of the proposed method.

Numerical methods for solving large-scale systems of differential equations

Abstract: In this paper, we propose two new methods to solve large-scale systems of differential equations, which are based on the Krylov method. In the first one, the exact solution with the exponential projection technique of the matrix. In the second, we get a new problem of small size, by dropping the initial problem, and then we solve it in ways, such as the Rosenbrock and the BDF. Some theoretical results are presented such as an accurate expression of the remaining criteria. We give an expression of error report and numerical values to compare the two methods in terms of how long each method takes, and we also compare the approaches.

Weighted $$p(\cdot )$$ p ( · ) -Laplacian problem with nonlinear singular terms

Abstract: In the present work, we prove an existence and uniqueness result of solutions to a quasilinear elliptic problem with nonlinear singular terms in the weighted Sobolev space. The equation that we consider is the following $$\begin{aligned} -\Delta _{p(\cdot )}^{\omega } u+\beta (u)=\frac{f(x)}{u^{\alpha }}, \end{aligned}$$ where $$\alpha \ge 1$$ , $$\beta $$ is a continuous non decreasing surjective real function on $${\mathbb {R}}$$ , f is a nonnegative function belonging to the Lebesgue space $$L^{m}(\Omega )$$ and $$m\ge 1$$ .