Normal rat pregnancy is characterized by plasma volume expansion due to renal sodium retention and is associated with a blunted response to natriuretic stimuli, such as atrial natriuretic peptide (ANP). ANP signals via cGMP, and phosphodiesterases (PDE) inactivate cGMP and terminate the natriuretic response. We previously reported that increased medullary PDE-5 activity occurs in rat pregnancy,...

In this paper, a computational intelligence method is used for the solution of fractional optimal control problems (FOCP)'s with equality and inequality constraints. According to the Ponteryagin minimum principle (PMP) for FOCP with fractional derivative in the Riemann- Liouville sense and by constructing a suitable error function, we define an unconstrained minimization problem. In the optimiz...

This paper presents a new numerical method to solve time fractional Fokker-Planck equation. The space dimension is discretized to the Gauss-Lobatto points, then we apply pseudo-spectral successive integration matrix for this dimension. This approach shows that with less number of points, we can approximate the solution with more accuracy. The numerical results of the examples are displayed.

This paper presents a numerical method for PDE-constrained optimization problems. These problems arise in many fields of science and engineering including those dealing with real applications. The physical problem is modeled by partial differential equations (PDEs) and involve optimization of some quantity. The PDEs are in most cases nonlinear and solved using numerical methods. Since such nume...

In this note we present a multigrid preconditioning method for solving quadratic optimization problems constrained by fractional diffusion equation. Multigrid methods within the all-at-once approach to solve first order optimality Karush–Kuhn–Tucker (KKT) systems are widely popular, but their development have relied on underlying being sparse. On other hand, most discretizations, matrix represe...

In this paper we propose a state estimation approach for linear parabolic Partial Differential Equations (PDE) with uncertain parameters. It is based on an extension of the Galerkin projection method. The extended method models projection coefficients, representing the state of the PDE in some basis, by means of a Differential-Algebraic Equation (DAE). The original estimation problem for the PD...

Abstract

Validated continuation was introduced in [4] as means of checking that the classical continuation method applied to a Galerkin projection of a PDE provides a locally unique equilibrium to the PDE of interest. In this paper we extend the numerical technique to include a parameter that leads to better bounds on the errors associated with the Galerkin truncation. We test this method on the Swift-H...